ArticlePDF Available

Caching Efficiency Maximization for Device-to-Device Communication Networks: A Recommend to Cache Approach

Authors:
  • Hong Kong Metropolitan University

Abstract and Figures

Edge side caching assisted device-to-device (D2D) communication has been acknowledged as a promising technique to alleviate the heavy burden of backhaul transmission link and to reduce the network latency. However, the effectiveness of caching strategies at the network edge is highly dependent on the distribution of individual user's content preference. To fully attain the benefits of edge caching, some proactive mechanisms shall be considered. Among which, recommendation performs noticeably well due to its capability of reshaping the content request probabilities of different users, which in turn affects the cache decision significantly. In this work, we quantitatively investigate how recommendation can be applied to enhance the caching efficiency of D2D enabled wireless content caching networks. And for that, the cache hit ratio maximization problem for a generic network model is formulated taking into account the requirements of each user's personalized recommendation quality, recommendation quantity and cache capacity. Then, we show that the optimal recommendation and caching policies which jointly maximize the cache efficiency is NP-hard to compute. Further, a time-efficient sub-optimal algorithm is designed, which works in an iterative manner and has provable convergence guarantee as well as polynomial time complexity. Monte-Carlo simulation results demonstrate the convergence performance of our proposed joint decision algorithm and its cache efficiency improvements compared to extensive benchmarks.
Content may be subject to copyright.
1
Caching Efficiency Maximization for
Device-to-Device Communication Networks: A
Recommend to Cache Approach
Yaru Fu, Lou Sala¨
un, Xiaolong Yang, Wanli Wen, and Tony Q. S. Quek
Abstract—Edge side caching assisted device-to-device (D2D)
communication has been acknowledged as a promising technique
to alleviate the heavy burden of backhaul transmission link and
to reduce the network latency. However, the effectiveness of
caching strategies at the network edge is highly dependent on
the distribution of individual user’s content preference. To fully
attain the benefits of edge caching, some proactive mechanisms
shall be considered. Among which, recommendation performs
noticeably well due to its capability of reshaping the content
request probabilities of different users, which in turn affects
the cache decision significantly. In this work, we quantitatively
investigate how recommendation can be applied to enhance
the caching efficiency of D2D enabled wireless content caching
networks. And for that, the cache hit ratio maximization problem
for a generic network model is formulated taking into account
the requirements of each user’s personalized recommendation
quality, recommendation quantity and cache capacity. Then, we
show that the optimal recommendation and caching policies
which jointly maximize the cache efficiency is NP-hard to com-
pute. Further, a time-efficient sub-optimal algorithm is designed,
which works in an iterative manner and has provable convergence
guarantee as well as polynomial time complexity. Monte-Carlo
simulation results demonstrate the convergence performance of
our proposed joint decision algorithm and its cache efficiency
improvements compared to extensive benchmarks.
Index Terms—Content caching, device-to-device (D2D) com-
munications, caching hit ratio, recommendation mechanism, NP-
hardness.
This work was supported in part by the Hong Kong President’s Adviso-
ry Committee on Research and Development (PACRD) under Project No.
2020/1.6, in part by the National Natural Science Foundation of China (NSFC)
under Grants No. 61971239 and No. 61771427, in part by the National
Key Research and Development Project under Grant No. 2020YFC1511701,
in part by the National Research Foundation, Singapore and Infocomm
Media Development Authority under its Future Communications Research
& Development Programme. Any opinions, findings and conclusions or
recommendations expressed in this material are those of the author(s) and
do not reflect the views of National Research Foundation, Singapore and
Infocomm Media Development Authority. (Corresponding author: Xiaolong
Yang.)
Y. Fu is with the School of Science and Technology, The Open University
of Hong Kong, Hong Kong, 999077, China (Email: yfu@ouhk.edu.hk).
L. Sala¨
un is with Bell Labs, Nokia Paris-Saclay, 91620 Nozay, France (e-
mail: lou.salaun@nokia-bell-labs.com).
X. Yang is with the School of Information and Communication Engineering,
Beijing Information Science and Technology University, Beijing, 100101,
China, and with the Key Laboratory of Modern Measurement and Control
Technology, Ministry of Education, Beijing Information Science and Technol-
ogy University, Beijing 100101, China. (e-mail: xiaolongyang@bistu.edu.cn).
W. Wen is with the College of Communication Engineering, Chongqing
University, Chongqing 400044, China (e-mail: wanli wen@cqu.edu.cn).
Tony Q. S. Quek is with the Dept. of Information Systems Technology and
Design, Singapore University of Technology and Design, Singapore (e-mail:
tonyquek@sutd.edu.sg).
I. INTRODUCTION
The rapid evolution of wireless communication technologies
as well as the termination techniques has trigged the explosive
growth of mobile data traffic. In accordance with the cutting
edge Ericsson mobility report [1], the mobile data traffic per
month is forecast to increase to 160 Exabytes (EBs) in 2025
from 38 EBs each month in 2019, pushing the endurance
to the limits of our current cellular networks architecture.
To address this issue, caching at the network edge side has
been acknowledged as one of the promising solutions [2],
[3]. More precisely, the popular contents can be stored by
the cache entities in mobile terminals and shared with neigh-
bor subscribers via device-to-device (D2D) communications,
making a substantial part of preferred content items ubiquitous
to the consumers. From this point of view, the construction
of the complicated wireless transmission links is not always
necessary for each content requesting. As a consequence, the
average content delivery latency and the backhaul transmission
load are reduced and alleviated. In recent years, D2D caching
networks have received extensive attentions [4]–[13]. To be
more specific, the performance comparison of D2D caching
and small cell base station (BS) caching is investigated in [4]
with the information of content popularity and spatiotemporal
request correlation taken into account. Thereof, the authors
reveal that D2D caching provides higher opportunity to serve
more users requests simultaneously via short-distance cache-
enabled D2D communication, especially when the user density
is high. In [5], the social-aware rate based content sharing
mode selection scheme for D2D caching system is studied
to maximize the weighted link capacity. The formulated op-
timization problem has been transformed to a submodular
welfare problem, which was solved by a distributed algorithm.
The joint cache placement and content delivery is investigated
in [6] to maximize the content successful offloading ratio.
Simulation results shown the efficacy of joint optimization.
The authors in [7] investigate the cache placement for D2D-
assisted cellular networks to maximize the achievable caching
revenue by a multi-winner auction approach. Thereof, several
decision-making algorithms with different time complexities
are developed. It is explicitly demonstrated by [8] that with
the prior information of users’ preference distribution, the
optimized caching placement for D2D networks achieves
significant improvement on content access delay and traffic
offloading gain. It is noteworthy that the contents can be
partially cached in [8], which is totally different from the
2
caching mechanism in [4]–[7], [9]–[13], where the caching
decision indicator of each item is a Boolean variable. Since
the cache placement algorithms for D2D caching network
always have huge computational complexity due to the large
size of users set and the contents library, clustering algorithms
are adopted in [9] and [10] to reduce problem’s dimensions
via bundling users into different small-size groups. With the
obtained clusters, cache decision is made to optimize various
objectives. Specifically, [9] targets at minimizing the average
content delivery latency while [10] aims to maximize the cache
hit ratio of users within each cluster. Recent works [11]–[13]
apply machine learning techniques into D2D caching networks
to do cache placement and user preference estimation.
Recommendation, on the other hand, has the capability of
reshaping the content request probabilities of different users,
which deeply influence the caching efficiency. It was precisely
demonstrated that the video view of YouTube and Netflix
induced by recommendation account respectively for 50% and
80% of the total views [14]–[16]. Thereby, considering caching
and recommendation independently cannot reach their full
benefits. Recommendation and caching are synergistic with
each other. Indeed, recommendation influences the content
request behaviors of users, which in turn affects the cache
decision making. In a nutshell, to construct user-friendly and
network-friendly wireless content caching systems, a coop-
erative working mechanism should be considered between
cache decision making and recommendation optimization.
Nevertheless, in existing wireless architectures, the recom-
mendation and content caching are in the charge of two
independent entities, i.e., the third-party content provider and
the telecommunication operators, respectively. Fortunately, the
fusion of roles like content providers and telecom operators
is speeding up and becomes more and more evident, making
the joint optimization become a reality. Chatzieleftheriou et
al. in [17] first propose the application of recommendation in
wireless content caching networks and consider the interplay
between caching and recommendation. This idea is extended
to generic cache-assisted small cell networks in [18], and it
is demonstrated that through recommendation-aware caching,
higher cache hit ratio can be obtained. Recognizing that users’
association affects the cache hit, a joint user association,
caching, and recommendation decision-making problem is
investigated in [19]. Simulation results show the validity
of user association in terms of improving system’s cache
efficiency. Later, many studies are made to investigate the
joint recommendation and cache optimization under extensive
performance metrics [20]–[25]. To be more specific, the suc-
cessful offloading probability maximization problem is studied
via jointly optimizing caching at the BS and personalized
recommendation at users in [20], [21]. Thereof, the authors
characterize the successful offloading ratio as the probability
that a requested file of a user can be retrieved from the content
provider triumphantly, i.e., the received signal-to-interference-
ratio (SIR) is no less than a pre-determined threshold. In [22],
[23], the cache hit ratio maximization problem for content
caching based networks with recommendation is investigated.
Specifically, in [22], a cache-aware recommendation algorithm
is proposed for the current economic ecosystem, wherein
the collaboration between network and content provider was
not required. Moreover, departing from the assumption of
hard cache hits in various existing works, [23] introduces
the concept of soft cache hits, in which, some related and
locally cached items will be recommended to user given that
his/her requested contents are not available. It is shown that
soft cache hit achieves enhanced caching gains. In contrast
to [17]–[23], where single content request mode is adopted,
the authors of [24] optimized the recommendation to obtain
the minimum caching cost of a sequential-content-access
based caching network. Nevertheless, the cache placement
optimization is neglected in [24], which is done by [25].
All the aforementioned works [17]–[25] focus on scenarios
where caching is conducted at the BSs. For user side caching,
[26] studies the data offloading ratio maximization problem
for cache enabled mobile social networks, whereas, cache
placement can only be implemented at important users (IU),
which is defined as the users who act as a helper to provide
contents for their adjacent subscribers. The authors applied the
notion of recommendation, in this case however, the effect of
recommendation mechanism on content request of users is not
quantitatively characterized in the problem formulation, as it
is done in this work.
In summary, new research is called to enable
recommendation-aware D2D-enabled wireless edge caching
networks. This motivates us to explore how recommendation
can be used to enhance the gains of caching approaches in
edge side cache networks with D2D communications. To the
best of our knowledge, investigating the caching efficiency
maximization problem for D2D enabled wireless content
caching systems from a perspective of recommend-to-cache
has never been addressed by existing works. We distinguish
the primary contributions of this work as follows:
We consider a generic D2D communication assisted
wireless content caching networks, wherein the role of
content provider for each user is modeled through the
social-aware value, which is further characterized by the
preference similarity as well as the distance between two
distinct users.
We quantitatively illustrate how recommendation and
caching affect the system caching efficiency mathemat-
ically. Based on it, the caching efficiency maximization
oriented joint recommendation and caching problem is
formulated with the consideration of individual user’s
recommendation quality, recommendation quantity and
cache capacity requirements.
We reveal the NP-hardness of the formulated maximiza-
tion problem with rigorous mathematical proof. To make
it tractable, we decouple the NP-hard problem into two
sub-problems and whereafter, two-side swapping oriented
algorithms are proposed to solve the sub-problems in
sequence. With the foregoing analysis, a time-efficient
suboptimal solution is designed, which works in an
iterative manner and has provable convergence guarantee.
The computational complexity of the proposed algorithm
is scrupulously analyzed as well.
Monte-Carlo simulation is implemented to validate the
3
D2D area
MBS
D2D area
Wireless
communication
link
User
D2D link
User
Cloud Server
Backhaul
link
Cache
Fig. 1. System model of the device-to-device (D2D) assisted wireless content
caching network. Thereof, users’ content requests are jointly determined by
their inherent preference as well as the system recommendation mechanism.
convergence performance of our designed algorithm and
highlight its caching efficiency enhancements when com-
pared to that of various baselines.
The rests of this paper are organized as follows: In Section
II, the architecture of our D2D assisted wireless content
caching network is introduced. Both the mechanisms on rec-
ommendation and the definitions on caching efficiency are
presented in Section III. Therein, the computing method of
social-aware value between D2D users is elaborated as well.
With the above mentioned preliminaries, the caching efficien-
cy maximization oriented joint recommendation and caching
decision problem is formulated in Section IV. In Section V,
we reveal that the formulated maximization problem is NP-
hard with rigorous mathematical proof. To solve the intractable
problem efficiently, a time-efficient sub-optimal algorithm is
designed in Section VI. Numerical results are presented in
Section VII to show the validity of our joint recommendation
and caching strategy. In the end, we summarize this work and
propose several possible future research directions.
II. SY ST EM MO DE L
In this section, we first introduce the architecture of our
cache aided device-to-device (D2D) communication network.
Afterwards, the caching model at each subscriber is elaborated.
A. Network Description
As illustrated in Fig. 1, we consider a D2D assisted wireless
content caching system, in which a macro base station (MBS)
servers Kuniformly distributed users within its disk region.
It is assumed that the users have the capabilities of content
caching, i.e., each user is equipped with a cache entity of
different size. Denote by K={1,2, . . . , K}the index set of
all the subscribers. In addition, let Bkbe the cache capacity
of subscriber k, where k∈ K. Our system includes Ncontent
items, which can be distinct for different macro cells. Define
N={1,2, . . . , N }as the index set of all the items. For n
N, let Lnin bits denote the size of content n. Moreover, we
define D
kas the index set of all users that are located within
user k’s D2D communication region, where k∈ K. Without
otherwise stated, in the following parts of this work, the set
D
kof user kincludes kitself. Furthermore, we declare that
both the MBS and the users are equipped with single antenna.
Each user can request his/her intended content from its
local cache given that the requested content of user khappens
to be cached in its local storage, the construction of D2D
communication link or wireless communication link is not
needed. Otherwise, user kwill broadcast the request to its D2D
neighbors1. Suppose that some of the neighbors have this item
in their storages, user kwill download this content through the
neighbor that induces the largest social-aware value2via D2D
communication link instead of creating complicated wireless
channels with MBS. A wireless communication link will be
established between MBS and user kgiven that the intended
item is not cached by the local storage and all the possible
D2D providers of user k, i.e., this content will be retrieved
from the cloud server by MBS. To be more specific, after
receiving the requests from users, MBS first downloads the
required contents from the cache of cloud content provider
and then feedbacks the items to the corresponding users.
It is noticeable that the communication between MBS and
the content servers is conducted via backhaul link. Besides,
it is assumed that the content provider’s servers can offer
any requested items from the users, which can be seen as a
backup content delivery mode. Intuitively, the cache enabled
D2D communication is capable of alleviating the workload of
backhaul links.
B. Caching at Users
In this subsection, we discuss the caching model at different
users. For k∈ K and n N , define the binary indicator ck ,n
as the caching decision of user kin terms of content item n.
Specifically, ck,n = 1 means user khas item nin its cache
and ck,n = 0 otherwise. Under the cache size constraint, we
have
n∈N
ck,nLnBk, k ∈ K.(1)
Before ending this section, we declare that the radio resource
adopted by D2D communication as well as that used by
wireless communication are orthogonal with each other. Since
the radio resource for wireless communication links as well
as the capacity of backhaul links are limited3, our system is
inclined to pose less content requests to the MBS via jointly
optimizing the caching deployment and the recommendation
decision for each subscriber. It is worth mentioning that even
though the cache capacity of mobile user is in general not very
large, the cache storage of all the mobile devices can generate
1Note that the D2D communication coverage region of a user is limited.
Thereby, the user can only communicate with its neighbors located within its
D2D region.
2The definition of social aware rate between two distinct users will be
specified in Section III-B
3Even though D2D communication also needs to use radio resource, the
communication cost is relative small due to its short distance when compared
to that of the communications between users and MBS, which always have
large distance-dependent path loss.
4
a large virtual and unitive cache space. How to reap the full
benefits of the cache space is the emphasis of this article. In
addition, the radio resource management with fixed caching
and recommendation decision for our system can be conducted
via following the conventional resource management schemes
in cache based D2D systems [27].
III. REC OM ME NDATI ON MECHANISM AND CACHE
EFFIC IE NC Y
In this section, we first illustrate the notion of user pref-
erence distribution. Then, the concept of social-aware value
between users is introduced. Subsequently, we present our de-
signed recommendation mechanism4as well as the associated
content request distribution of each user, wherein the user-
specific recommendation quality is taken into account. Finally,
the considered effectiveness metric for our cache aided D2D
system is explained.
A. User Preference Distribution
We assume that the Ncontent items belong to Mthemes,
indexed by M={1,2, . . . , M}. It is important to note that
the Mthemes can be regarded as the feature sets that capture
different items in content library N. In addition, the definition
of theme can be diverse. For instance, the generalized concept
“video” can be classified as different categories, e.g., variety
entertainment, movie, talk show, music, etc. Nevertheless, the
category “movie” can be further divided into several sub-
themes, e.g., love, science fiction, comedy, animated cartoon,
history, and war movies, etc. The contents library in this work
can be either a main class or a distinct category. The specifics
of such classification is not the main focus of this paper.
For n∈ N and m∈ M, define f
n(m)[0,1] as the score
of item nin feature m, which represents how much item n
is correlate to theme m. For each content item, we normalize
these scores over all the themes and obtain the normalized
feature value of item non theme mas follows:
fn(m) = f
n(m)
M
m=1 f
n(m), m ∈ M.(2)
In addition, let fn= (fn(1), fn(2), . . . , fn(M)) be the feature
vector of item n.
Similarly, for user k, a feature vector over all the themes
is characterized as well. For k K and m∈ M, let
f
k(m)[0,1] represent the score of user kin category m,
which indicates how much user klikes the contents of theme
m. Thereby, we can obtain the feature vector of user k, which
is denoted by fk= (fk(1), fk(2), . . . , fk(M)), whose m-th
component is calculated as follows:
fk(m) = f
k(m)
M
m=1 f
k(m), m ∈ M.(3)
4Unless otherwise stated, the recommendation studied in this paper is
task-based [28]. More precisely, the recommendation is performed to return
optimized objective value in a specific task. Considering a time period of
a few hours or half of a day, the preference for each content per user can
be treated as fixed. In other words, the individual user’s recommendation
decision, and the cache placement are done once for such interval of time to
optimize system’s caching efficacy.
In this work, we assume that the aforementioned feature
vectors are prior information since they can be estimated
by content provision sites in accordance with the histori-
cal information of users’ contents requests and downloads,
as suggested by [11], [29], [30]. Particularly, via modeling
the user’s request behavior by probabilistic latent semantic
analysis (pLSA) and estimating the associated parameters by
the expectation maximization algorithm, the authors in [11]
predict the users’ preference distribution based on a Movielens
data set. Details are omitted here to avoid redundancy.
As far as the heterogeneity of different users, we assume
that each user has personalized preferences to the content items
in N. For k∈ K and n N , define apref
k,n [0,1] as the
preference of user kto item n, which can be acknowledged
as the probability that user kasks for item n. Based on [18],
the inherent preference of user kin terms of item ncan be
jointly modeled by the feature vectors of kand n, i.e., fkand
fn, respectively. We adopt in this work the same generation
procedure as in [18] to construct the individual preference
distribution of user kover all the contents. It is characterized
by the cosine similarity index of the aforementioned two
vectors fkand fn, and is expressed as follows:
˜apref
k,n =M
m=1 fk(m)fn(m)
M
m=1 (fk(m))2M
m=1(fn(m))2
, k ∈ K, n N .
(4)
We normalize the values of ˜apref
k,n over all the items in Nfor
each user k, where k∈ K. Then, the preference distribution
of user kin terms of content nis quoted below:
apref
k,n =˜apref
k,n
N
n=1 ˜apref
k,n
, n N ,(5)
where ˜apref
k,n is given in (4). For notation simplicity, apref
k=
(apref
k,1, apref
k,2, . . . , apref
k,N )is used to represent the preference dis-
tribution vector of user k, where k∈ K.
B. Social-aware Value
In practical D2D systems, the individual users are in general
intend to cache the content items that are ranked in their top
preferences. In other words, users are not willing to cache the
contents that are more attractive to other neighbor users but not
highly desired by themselves. This is reasonable, especially
when considering the selfish nature of human behaviour. To
address this issue, in this work, we assume that user k
only provides possible D2D-oriented supports for its socially
connected users. For k∈ K, the socially-aware subscribers of
user kshould satisfy the following criteria:
i. Located within the D2D communication region of mobile
user k.
ii. The social-aware value associated with user kis no less
than a pre-determined threshold, which is denoted by ¯
Vk
for k∈ K. The threshold is chosen by the user itself,
which indicates how selfish the user is.
The social-aware rate between user kand user k, denoted by
Vk,k, is characterized by two elements, namely the distance
between this pair of users and the preference correlation
5
User 1
1
2
3
4
5
5
4
1
3
2
User 2
1
2
3
5
4
User 3
ܸ
ଵǡଷ
User 4
2
3
1
4
5
ܸ
ଵǡସ
ܸ
ଷǡସ
ܸ
ଶǡଷ
Fig. 2. An example of socially-aware D2D communication system with
4 users and 5 contents, where the table represents the contents preference
ranking of each subscriber.
of these two users, which are defined as dk,kand Sk,k,
respectively. With above definitions, Vk,kis given as follows:
Vk,k,Sβ
k,k/dα
k,k,(6)
where k, k∈ K.αand βrepresent the weights of preference
similarity and the distance, respectively. In addition, they
satisfy α+β= 1. It is worth noting that, for user k, the
shorter distance to user kand the higher preference correlation
with user k, the larger value of social-aware rate Vk,k. An
example with 4 users and 5 contents is illustrated in Fig. 2.
From which, it is easy to see that V1,3is larger than V2,3due
to the shorter distance and higher similarity between user 1
and user 3 when compared to that between user 2 and user 3.
In this work, we apply the cosine similarity as in [31] to
determine the preference correlation between users kand k,
which is quoted below
Sk,k,apref
kapref
k
||apref
k|| × ||apref
k||,(7)
where ||x|| indicates the l2-norm of vector x.
Since user kcan only receive contents from the subscribers
that are socially correlated with himself or herself via D2D
communications, we define the social neighbor set of user k
as Dk. With aforementioned analysis, we have
Dk={k|k∈ D
k,and Vk,k¯
Vk}, k ∈ K.(8)
C. Recommendation Model
As above mentioned analysis, each user has an inher-
ent preference distribution to the content items in N, i.e.,
apref
k, where k∈ K. Each user will request its desired
contents following this distribution without other external
factors, e.g., recommendation. Otherwise, the requests will be
jointly determined by both the inherent preference and the
recommendation mechanism. In the following paragraph, the
recommendation model used in this article is introduced.
Given that the system conducts recommendations, the con-
tent request probability of each user will be definitely affected,
as discussed in [14]–[16]. Nevertheless, the investigation on
how the recommendation mechanism quantitatively affects the
content request of users is still in its infancy due to the
high complexity of human behavior. The authors in [18],
[32] have proposed some intuition or experiment oriented
methods. To be more specific, in [18] the ultimate content
request distribution of each user is designed as a convex
combination of the individual inherent preference distribution
and the recommendation probability distribution. Meanwhile,
the authors in [32] mapped the recommendations for user k
to a new distribution denoted by arec
k,n, where n N , and
the request probability of user kon item nis shaped as
max{arec
k,n, apref
k,n}. The recommended items for each user have
boosted request probabilities while the request probabilities
of the non-recommended items are decreased to guarantee
the request distribution remains normalized in the above
discussed two methods. In reality, the users may reject the
recommendations, especially when they do not identify the
quality of the recommended contents before they consume the
items. To characterize this feature, in this work, we follow
the model introduced in [17], and widely used, e.g. in [20],
[21]. We assume that user kaccepts the recommendations
with a probability denoted by xk[0,1]. In this aspect,
the rejection probability of user kto the recommendations
is (1 xk)[0,1]. In this work, it is assumed that xkis
a prior information and different mobile users have different
values of xkdue to their heterogeneities in personality.
D. User Content Request Distribution
In the subsection, we reveal how recommendation affects
the content request probability of each subscriber mathemat-
ically by following the footsteps in [17]. For k∈ K and
n N , define rk,n ∈ {0,1}as the binary indicator to
represent whether content nis recommended to user kor not.
In particular, rk,n = 1 if the content item nis recommended
to user kand 0 otherwise. In addition, let Rkbe the index
set of all the items that have been recommended to user k.
Therein, the cardinality of Rkis assumed to be Rk. It is
notable that Rkcan be taken as the recommendation quantity
of user k. This kind of setting is necessary, especially for the
screen size limited customers, e.g., mobile phones, iPad and
lap-top, etc. Since scrolling down for a long recommendation
list is not user friendly. Besides, we define areq
k,n as the
ultimate request probability of user kwith respect to item
nthat is jointly determined by its inherent preference as well
as the recommendation mechanism. Specifically, the request
probability of user kto the recommended item n∈ Rkis
expressed as follows:
ˆareq
k,n =rk,n apref
k,n
j∈Rkapref
k,j
=rk,napref
k,n
j∈N rk,j apref
k,j
,(9)
where k∈ K and n N . Meanwhile, the request probability
distribution of user kto the non-recommended item n∈ N \
Rkis quoted below:
˜areq
k,n =(1 rk,n )apref
k,n
j∈N \Rkapref
k,j
=(1 rk,n)apref
k,n
j∈N (1 rk,j )apref
k,j
.(10)
Summarizing the above mentioned two-fold analysis into a
uniform formula, we obtain the request probability of user k
6
in terms of item nas follows:
areq
k,n =xkˆareq
k,n + (1 xkareq
k,n
=xk
rk,napref
k,n
j∈N rk,j apref
k,j
+ (1 xk)(1 rk,n)apref
k,n
j∈N (1 rk,j )apref
k,j
,
(11)
where k∈ K and n N . Thereof, ˆareq
k,n and ˜areq
k,n are well
defined in (9) and (10), respectively.
Remark 1. Based on (11), it is easy to check that the contents
request distribution of user k,areq
k,n for n N , remains
normalized, where k∈ K.
E. Personalized Recommendation Quality
In this subsection, we give the definition of recommendation
quality, which is an important personalized metric in recom-
mendation system. Specifically, even though the recommenda-
tion system can reshape the content request probability of each
user, the inherent preference distribution of users should also
be taken into consider to avoid the psychological inversion of
users [33]. To alleviate this issue, a user-specific psychological
threshold is set for each subscriber to measure the quality of
the recommendation, which is denoted by Qk, where k∈ K.
Under the recommendation quality constraint, we have
n∈N
rk,napref
k,n Qk, k ∈ K,(12)
where apref
k,n is defined in (5). In addition, we assume the value
of Qkis a prior information for k∈ K, which can be estimated
from the interactive response system provided by content
service companies. A simplified example, the customers will
be labeled according to their historical behavior [34], the ones
that have relatively picky labels will be assign a Qkwith
higher value, while the users with casual personality will
be given a lower threshold. Moreover, this value can also
be pre-determined by user itself to represent its personalized
requirement. Details about the methodologies on setting the
value of Qkare not explicitly discussed here.
F. System Effectiveness
In this subsection, we discuss the system performance
metric of this work. On one hand, for the mobile users, the
associated requirement is that their requested contents can
be provided by the edge caches. On the other hand, the
less content requests from users the lighter burden of the
wireless communication links and the backhaul transmission
links, which in turn reduces the content access latency and
improves users quality of experience. The above mentioned
two aspects can be well satisfied with a high content hit ratio
(CHR), which is defined as the probability that the required
contents of subscribers are cached by their socially connected
mobile terminals. As a consequence, in this work, we define
CHR as our system performance measurement.
With aforementioned definitions, the CHR of user kin terms
of requesting content item nis quantified below:
CHRk,n =areq
k,n ×I(
k∈Dk
ck,n),(13)
where k∈ K,n N . In addition, I(x)is an indicator
function, and it is defined as follows:
I(x) = 1if x > 0
0otherwise.(14)
Moreover, the definition of areq
k,n is given in (11). According
to (13), we can see that, from user k’s own selfish point of
view, caching the items within its effective D2D region that
has large value of areq
k,n increases CHR of user kdramatically.
However, the decision will be definitely affected when taking
the other socially connected users’ content request probability
into account. In addition, the caching decision of user kwill
also be significantly affected by the caching states of the users
within its social neighbor set, referred to as Dk. Thereby, how
to apply the cache resource of all the mobile devices in a
federated and effective manner should be well investigated.
IV. JOI NT RECOMMENDATION AND CACHE DECISION
PROB LE M FOR MU LATI ON
In this work, we target at maximize the CHR of al-
l subscribers via jointly optimizing content caching and
recommendation decisions for each individual user. Let
ck= (ck,1, ck,2, . . . , ck,N )and c= (c1,c2, . . . , cK)be
the cache decision of user kand the cache decision vec-
tor of the network, respectively. Similarly, define rk=
(rk,1, rk,2, . . . , rk,N )and r= (r1,r2, . . . , rK)as the rec-
ommendation strategy vectors of user kand the system,
respectively. With the definitions, the CHR maximization ori-
ented joint cache placement and recommendation decision for
cache enabled D2D communication network is mathematically
formulated as follows:
maximize
r,c
k∈K
n∈N
CHRk,n P(1)
subject to
C1:
n∈N
ck,nLnBk, k ∈ K,
C2:
n∈N
rk,napref
k,n Qk, k ∈ K,
C3:
n∈N
rk,n =Rk, k ∈ K,
C4:rk,n ∈ {0,1}, k ∈ K, n N ,
C5:ck,n ∈ {0,1}, k ∈ K, n N ,
where CHRk,n in the objective function is well given in
(13). In addition, C1indicates that the cache capacity of user
kcannot exceed its storage budget. Besides, C2represents
users recommendation quality requirements as aforementioned
analysis. Moreover, C3shows the constraint for the recommen-
dation quantity per user, where Rkrepresents the maximum
number of the recommended items for user k, where k∈ K.
Furthermore, C4and C5depict the binary property of the
decision variables. For simplicity, we denote the formulated
CHR maximization problem as P(1), which is a non-convex
integer optimization problem, whose complexity is mathemat-
ically examined in next section.
7
V. PROBLEM COMPLEXI TY AN ALYS IS
In this section, we prove the NP-hardness of the content hit
ratio maximization problem P(1) with rigorous mathematical
proof. Details are presented in the following Theorem:
Theorem 2. P(1) is NP-hard.
Proof: The idea of the proof is to construct a polynomial-
time reduction mapping any instance of an NP-hard problem
to an instance of P(1). We say that P(1) is NP-hard according
to the transitivity of reduction [35]. The NP-hard problem
considered here is the multiple knapsack problem (MKP),
which has been well studied in [36]. It is defined as follows:
maximize
y
K
k=1
N
n=1
pnxk,n (MKP)
subject to
C
1:
N
n=1
wnxk,n Wk, k ∈ K,
C
2:
K
k=1
xn,k 1, n N ,
C
3:xn,k ∈ {0,1}, n N , k ∈ K,
where Kdenotes the number of knapsacks, and Nis the
number of items. Parameters wnand pnrepresent the weight
and profit of item n, respectively. Besides, Wkdenotes the
capacity of the k-th knapsack in constraint C
1. The decision
variable xn,k is set to 1if and only if item nis assigned to
the k-th knapsack. Constraint C
2ensures that each item nis
assigned to at most one knapsack.
Given an instance of MKP with the aforementioned param-
eters, we construct an instance of P(1) with Kusers and
Nitems. For each user k∈ K and item n N , we set:
apref
k,n ,pn
N
i=1 pi,xk,1,Dk,K,Ln,wn,Bk,Wk,
Qk,1, and Rk,N. Note that the user preference
distribution is normalized, i.e., n∈N apref
k,n = 1, for all k∈ K,
to be consistent with definition (5). Problem P(1) can be now
written as:
maximize
r,c
k∈K
n∈N
CHRk,n (MKP)
subject to
C
1:
n∈N
wnck,n Wk, k ∈ K,
C
2:
n∈N
rk,n
pn
N
i=1 pi
1, k ∈ K,
C
3:
n∈N
rk,n =N, k ∈ K,
C
4:rk,n ∈ {0,1}, k ∈ K, n N ,
C
5:ck,n ∈ {0,1}, k ∈ K, n N .
Constraints C
2,C
3and C
4imply that rk,n = 1, for all
users kand items n. Hence, the objective function of P(1)
becomes:
k∈K
n∈N
CHRk,n =
k∈K
n∈N areq
k,n ×I(
k∈K
ck,n),(15)
=
k∈K
n∈N pn
N
i=1 pi
×I(
k∈K
ck,n),(16)
=K
N
i=1 pi
n∈N pn×I(
k∈K
ck,n).(17)
Equation (15) comes from the fact that Dk,K. We then
derive (16) from the definition of areq
k,n, the choice of apref
k,n,xk,
as well as from rk,n = 1 due to constraints C
2to C
4. We
multiply the objective function (17) by N
i=1 pi/K to get the
following equivalent problem:
maximize
r,c
n∈N pn×I(
k∈K
ck,n)P(1)
subject to
C
1:
n∈N
wnck,n Wk, k ∈ K,
C
5:ck,n ∈ {0,1}, k ∈ K, n N .
Since the social neighbor sets contain all users, i.e., Dk,
K, each item only needs to be cached by one user in an optimal
solution of P(1). More precisely, we claim that there exists
an optimal solution c
k,n satisfying k∈K c
k,n 1, for all
n N . Indeed, let us consider an optimal solution such
that c
k1,n =c
k2,n = 1, for some n∈ N and k1, k2∈ K.
We have I(k∈K c
k,n)=1. By setting c
k2,n = 0, the
indicator function remains the same, i.e., I(k∈K c
k,n) = 1.
Therefore, when only one user cache item n, the objective
value remains optimal and C
1,C
5are still satisfied. Finding
the optimal value of P(1) is thus equivalent to finding the
optimal value of the following problem P′′(1).
maximize
r,c
k∈K
n∈N
pnck,n P′′(1)
subject to
C
1:
n∈N
wnck,n Wk, k ∈ K,
C
5:ck,n ∈ {0,1}, k ∈ K, n N ,
C6:
k∈K
ck,n 1, n N ,
where C6has been added to ensure that each item is cached
by at most one user. We see that problem P′′(1) is equivalent
to MKP by rewriting ck,n as xk,n. Hence, we have constructed
a polynomial time reduction from any instance of the MKP to
an instance of P(1). We derive that P(1) is NP-hard due to
the NP-completeness of MKP [36].
VI. CACHING AND REC OM ME NDATIO N OPTIMIZATION
ALGORITHMS DESIGN
In this section, the joint caching and recommendation opti-
mization for P(1) is studied, where we target at solving it in
8
a time-efficient manner since obtaining the optimal solution is
NP-hard. Towards this end, we first decouple P(1) into two
subproblems, i.e., cache placement with fixed recommendation
strategy and the recommendation decision under given caching
policy, respectively. Whereafter, the corresponding algorithm
for each subproblem is designed. Based on the two-tire anal-
ysis, a joint cache placement and recommendation decision
algorithm is proposed, which is proceed in an iterative manner
and has guaranteed convergence performance. In addition,
we prove that our proposed joint decision algorithm has
polynomial-time computational complexity.
A. Optimization of Caching Decision
In this subsection, the caching placement for problem P(1)
is investigated with the prior information of recommendation
decision, i.e., r. Given r,P(1) is reduced to the following
problem P(2) with objective function
max
c
n∈N
k∈K
areq
k,n ×I(
k∈Dk
ck,n),(18)
and subjects to the constraints C1and C5. In the objective
function of P(2), the content request probability areq
k,n is known
with fixed raccording to (11), where k∈ K and n N .
In addition, from (18), we see that Iis a function of c. For
simplicity, we rewrite I(k∈Dkck,n)as I(c). Note that P(2)
is an integer non-convex programming as well since I(c)
is non-convex5, which is still intractable to solve. To avoid
combinatorial complexity in obtaining the optimal solution,
we propose a suboptimal caching decision algorithm based
on the concept of two-sided exchange, which ensures a non-
decreasing system CHR from any arbitrary initial state. This
will benefit the convergence performance of our joint decision-
making algorithm.
Before detailing the proposed algorithm, some definitions
are clarified. Denote by Ekthe index set of the cached items
of subscriber k, where k∈ K. Note that Ekcan be mapped
to the caching decision vector of user k, i.e., ck. In detail,
ck,n = 1 if and only if n∈ Ek. For simplicity, we define the
mapping Ψ:Ekckas follows:
Ψ(Ek),ck,(ck,1, ck,2, . . . , ck,N ), k ∈ K.(19)
In addition, we define Vk=N \ Ekas the complementary set
of Ek, and let E={Ek|k∈ K} represent the caching policy
of the entire system. Similarly, another mapping Λ:E → cis
defined such that
Λ(E),c,(c1,c2, . . . , cK).(20)
Thereby, we now can write CHRk,n in the objective function
of P(2) as the function of Λ(E)and r. Besides, denote by
CHR(r,Λ(E)) the cache hit ratio of the system under the
caching strategy Λ(E)and given r. Specifically, we have
CHR(r,Λ(E)) =
k∈K
n∈N
CHRk,n(r,Λ(E)).(21)
With aforementioned discussions, we specify the definition
of the swap-blocking pair of subscriber kas follows:
5The detailed definition about the indicator function Iis given in (14).
Definition 3. Given a pair of items (ik, jk)where ik∈ Ekand
jk∈ Vk, respectively. We say (ik, jk)is a swap-blocking pair
suppose that C1under E
kas well as the following condition
CHR(r,Λ(E(k, ik, jk))) >CHR(r,Λ(E)) (22)
are satisfied, where E(k, ik, jk),{Ej|j K \ {k},Ek=E
k},
in which E
k,Ek\ {ik} ∪ {jk}.
We claim that the concept of swap-blocking adopted in
our problem derives from matching theory [37]–[39]. In ac-
cordance with Definition 3, the achievable cache hit ratio of
our system will increase given that the two-side exchange of
items in a swap-block pair is approved. Since the caching
policy of one subscriber affects the decisions of the other
users mutually, the caching deployments for all users should
be designed jointly. The proposed cache decision approach is
an iterative algorithm, where we assume that the initial cache
strategies of all users are based on the top-cache policy. In
particular, for subscriber k, it will cache the top-ranked items
based on its inherent preference distribution, apref
k, to make its
cache storage full, i.e., the following constraint
Bkmin
n∈Vk
Ln<
n∈N
ck,nLnBk
is satisfied.
In order to achieve a high content hit ratio, it is sensible to
approve the swapping of a pair items, denoted by (i
k, j
k),
that induces the largest objective value of problem P(2), i.e.,
(i
k, j
k),argmax
(ik,jk)⊂Sk,k∈K
CHR(r,Λ(E(k, ik, jk))),(23)
in which
Sk,{(ik, jk)|ik∈ Ek, jk∈ Vk}, k ∈ K.(24)
We repeat the two-side exchange oriented steps until no
swapping pair can be found. For the sake of simplicity, we
summarize the pseudo-code of the proposed cache decision
approach to P(1) under given recommendation policy in
Algorithm 1.
Algorithm 1 Cache placement algorithm
1: Given the pre-determined recommendation strategy r, the initial
cache decision vector c, and the auxiliary sets Skas expressed
in (24). In addition, denote by K=K.
2: repeat
3: Determine the pair (i
k, j
k)based on (23), i.e.,
(i
k, j
k) := argmax
(ik,jk)⊂Sk,k∈K
CHR(r,Λ(E(k, ik, jk))).
4: if (i
k, j
k)is a swap-blocking pair then
5: Let Ek,Ek\ {i
k}∪{j
k}.
6: Update ckin accordance with (19), i.e., ck:= Ψ(Ek).
7: else
8: Keep the current caching policy.
9: end if
10: Update Sk,Sk\ {(i
k, j
k)}
11: if Sk=then
12: Denote K,K\ {k}.
13: end if
14: until No swap-blocking pair can be found
15: return the caching strategy ckfor k∈ K.
9
B. Optimization of Recommendation Decision
We investigate the optimization for recommendation deci-
sion, r, with fixed caching strategy, c, in this subsection. It
is worth noting that, given c, the indicator function I(c)is
determined, which can be acknowledged as the availability of
content item nto subscriber kvia D2D-enabled edge caching,
where k∈ K and n N . Thereby, how to conduct the
recommendations is vital to maximize the CHR of the system
since raffects the coefficients of I(c).
In accordance with the definition of content request proba-
bility in (11), the recommendation optimization for subscriber
kis independent with the other users’ strategies. Therefore,
the recommendation decision for all the subscribers with fixed
ccan be divided into Kparallel subproblems. Each user
solves its own recommendation decision making subproblem.
Without loss of generality, we choose user kas an example.
For user k, (s)he needs to optimize rkto maximize its caching
hit ratio. Define Uk=N \ Rkas the supplementary set of the
recommended contents set of user k, i.e., Rk. We assume the
top-Rkmost preferred items based on the inherent preference
in (5) are selected as the initial recommended contents of
mobile user k, where k∈ K. Define the mapping Φ:Rkrk
as follows:
Φ(Rk),rk,(rk,1, rk,2, . . . , rk,N ).(25)
To be more specific, rk,n = 1 if n∈ Rkand 0 otherwise.
Denote by CHRk(Φ(Rk),c)the cache hit ratio of user k
whose recommended items fall into Rk, therein the caching
decision is c. With aforementioned definitions, we have
CHRk(Φ(Rk),c),
n∈N
areq
k,n ×I(c).(26)
Based on (11), it is easy to see that the request distri-
bution of user k, i.e., areq
k,n, is a non-convex function of
the recommendation vector rk. Therefore, to simplify the
algorithm, we propose a matching theory oriented method
to do the recommendation decision optimization, which has
similar properties to the methodology used in the caching
decision problem. Hereafter, we first give the definition of
a swap-blocking pair for user kvia exchanging the items
between sets Rkand Uk, and it is given as follows:
Definition 4. For any pair of contents (i, i)where i∈ Rk
and i∈ Uk, we say (i, i)is a swap-blocking pair provided
that C2under R
kas well as the following condition
CHRk(Φ(R
k),c)>CHRk(Φ(Rk),c)(27)
are satisfied, in which R
k,Rk\ {i} ∪ {i}.
Intuitively, the exchange of items iand i, which come from
sets Rkand Uk, respectively, resulting in an increased CHR
value for user k. Based on this observation, the recommenda-
tion optimization algorithm is designed, whose main idea is
to do the swapping one by one until no swap-blocking pair
can be found for each subscriber. For brevity, the two-side
swapping oriented recommendation decision methodology for
user kis concluded in Algorithm 2.
Algorithm 2 Recommendation decision algorithm for user k
1: Given the caching placement strategy cand the initial recom-
mendations set Rk. Define an auxiliary set as G={(i, i)|i
Rk, i∈ Uk}.
2: repeat
3: Select (i, i)⊂ G.
4: if (i, i)is a swap-blocking pair then
5: Let Rk=Rk\ {i}∪{j}.
6: Update rkbased on (25), i.e., rk:= Φ(Rk).
7: else
8: Keep the current recommendation pattern.
9: end if
10: Adjust G=G \ {(i, i)}.
11: until No swap-blocking pair can be found for user k
12: return the recommendation decision of user k, i.e., rk.
C. The Joint Optimization for Cache Placement and Recom-
mendation Decision
In this subsection, we discuss the joint cache placement and
recommendation decision algorithm based on the aforemen-
tioned two-fold analysis. Wherein, the convergence as well as
the complexity of the proposed approach are investigated.
At first, some definitions are presented. For k∈ K and
n N , define ck,n (t)as the cache decision of user kin
terms of content item nin the t-th iteration. In addition,
denote by ck(t) = (ck,1(t), ck,2(t), . . . , ck,N (t)) the caching
strategy of subscriber kin iteration t. Besides, let c(t) =
(c1(t),c2(t), . . . , cK(t)) be the caching policy of our method
in the t-th iteration. Moreover, it is assumed that c(0) is
set by the top-cache scheme as discussed in Section VI-A.
Similarly, we define r(t)as the recommendation decision in
the t-th iteration and set r(0) by the aforementioned top-
recommendation strategy. Furthermore, denote by CHR(r,c)
the objective function of P(1) under the optimized decisions
(r,c).
With the definitions, the joint optimization algorithm is
expressed as follows: in the t-th iteration, with the obtained
recommendation strategy r(t1) in the (t1)-th iteration,
we obtain the optimized caching policy c(t)in accordance
with Algorithm 1, in which the initial cache decision vector
(in line 1 of Algorithm 1) is set to be c(t1). Based on
the resultant c(t), we determine the updated recommendation
scheme r(t)according to Algorithm 2, wherein the initial
recommendation policy in line 1 of Algorithm 2 is assumed to
be r(t1). These kinds of settings guarantee the optimized
strategy results in a monotonously increased objective value.
We repeat the aforementioned steps until that the value of
CHR(r(t),c(t)) can not be further increased or the maximum
iteration number is reached. In the interest of conciseness, the
pseudo-code of our designed joint decision methodology is
summarized in Algorithm 3.
Lemma 5. The convergence of Algorithm 3 is warranted.
Proof: With foregoing analysis, it is easy to see that the
CHR of P(1) during the iteration is a monotonic increasing
sequence. According to (13), the objective value of P(1) is
upper bounded by K, the convergence is guaranteed [40].
In addition, the complexity of Algorithm 3 is elaborated in
the following proposition.
10
Algorithm 3 Joint cache and recommendation optimization
algorithm
1: Define the maximum iteration number as T. Determine r(0) by
the top-recommendation strategy, and initialize c(0) based on the
top-cache scheme. Let t= 1.
2: repeat
3: Obtain the caching police c(t)under fixed recommendation
policy r(t1) according to Algorithm 1. Therein, we claim
that, the initial caching strategy of Algorithm 1 is set as c(t
1).
4: Update the recommendation strategy r(t)with the obtained
caching strategy c(t)of last step in the light of Algorithm
2. It is notable that, in this step, the initial recommendation
decision in line 1 of Algorithm 2 is set to be r(t1).
5: Update t=t+ 1.
6: until CHR(r(t),c(t)) cannot be further increased or the maxi-
mum iteration number is reached, i.e., t>T
7: return the joint cache and recommendation decision strategy
(r,c)
Proposition 6. Since Algorithm 3 is constituted by the recom-
mendation optimization and the cache decision approaches,
i.e., Algorithm 2 and Algorithm 1, respectively, its complexity
shall be determined by these two algorithms. Specifically, the
complexity of Algorithm 1 is relates to the set size of Skfor
k∈ K due to the application of two-side swapping, which
can be attained as O(KN 2). Similarly, the time complexity of
Algorithm 2 is obtained as O(RkN).
Before ending this section, we declare that the binary vari-
ables are in general coupled in the optimization problems for
recommendation-aware caching networks, these problems are
very challenging to be solved. A commonly used methodology
is to decouple the variables, explore the solutions for each
individual subproblem, and alternatively optimize the differ-
ent types of variables. This research methodology has been
widely utilized by [17]–[21] and this work. More precisely,
the dynamic programming algorithm and a simpler heuris-
tic scheme are proposed to solve the cache placement and
recommendation decision subproblems, respectively, in [17].
Nevertheless, our cache decision subproblem is still a non-
convex and non-linear integer programming problem, which
cannot be solved by the proposed method in [17] directly.
Thereby, a match theory oriented algorithm is designed, which
ensures a non-decreasing system CHR from any arbitrary
initial state. This will benefit the convergence performance
of our joint decision-making algorithm. Similarly, our recom-
mendation decision-making subproblem is also a non-convex
integer problem since the objective function is non-convex to
r. Thus, to avoid combinatorial complexity in obtaining the
optimal solution, a two-side swapping method is designed,
which has similar properties to the method used in the caching
decision problem. Note that both the pure cache placement and
the pure recommendation decision-making subproblems are
linear integer programming problems in [17], which, however,
are non-convex integer problems in this paper.
VII. NUMERICAL RES ULTS
Monte-Carlo simulation is conducted in this section to show
the performance of our designed joint recommendation and
caching algorithm. The system parameters are summarized as
follows. The cell radius is set to be 250 m, where 20 users
uniformly distributed within its disk region, i.e., K= 20. The
D2D communication radius per user is assumed to be 25 m.
In addition, the contents number is set to be N= 50, which
are characterized by M= 10 themes. The feature vectors
of both users and contents are generated via a random walk
method. Without loss of generality, we assume each content
item has the same data size, which is normalized as 1, that
is Ln= 1 for n N . As a consequence, the cache capacity
of user kcan be set to be an integer number, and we assume
that the users have the same size storage, i.e., Bk=Bfor
k∈ K. Moreover, we consider the usage scenario where each
user has the same acceptance probability, the recommendation
size, the recommendation quality requirement and the social-
aware rate threshold, i.e., xk=X,Rk=R,Qk=Qand
¯
Vk=Vare satisfied for k∈ K, respectively. We declare
that our designed algorithm also appropriates for the scenarios
where Bk,xk,Rk,Qk,¯
Vkare disparate for k∈ K. Without
otherwise stated, in the simulation, we assume that X= 0.618,
Q= 0.08 and let αin (6) be α= 0.686, respectively [41],
[42]. Furthermore, for the sake of obtaining complete picture
of the research focus, we model the preference distribution of
each user as follows:
apref
k=win
kain
k+1win
kaout,(28)
where ain
krepresent the personalized content preference distri-
bution of subscriber k, the components of which are obtained
based on Section III-A, while aout represents the external
content preference distribution in accordance with the content
popularity, whose elements are generated according to the Zipf
distribution [8]. win
k[0,1] depicts the weight of the inherent
content preference distribution. Note that let win
k= 1 for
k∈ K, the preference distribution is exactly the one as defined
in Section III-A.
In addition, for performance comparison, the following
baselines are taken into considered:
Baseline 1: Top cache and no recommendation. In this
scheme, user kcaches the top preferred items based
on its inherent preference distribution, apref
k, to make its
cache storage full. In addition, no recommendation will
be conducted for each subscriber.
Baseline 2: Top cache and top recommendation. In this
method, the caching policy is the same as that in Baseline
1, while user kwill be recommended by the top-Rk
contents based on apref
k, where k∈ K.
Baseline 3: Homogeneous cache and top recommen-
dation. In this strategy, each user will cache the top
ranked items in accordance with all the users aggregated
preference to stuff up their caches. Thereof, the recom-
mendation scheme is the same as Baseline 2.
Baseline 4: Homogeneous cache and homogeneous rec-
ommendation. The caching scheme of Baseline 4 is
identical with that of Baseline 3, while each user k∈ K
will be recommended the top-Rkitems based on the
aggregated preference of all subscribers.
Revised CawR: In this strategy, the proposed CawR algo-
11
0 50 100 150
Iteration Index
8
10
12
14
16
18
Cache Hit Ratio
(a) V= 0.04.
0 50 100 150
Iteration Index
6
8
10
12
14
16
Cache Hit Ratio
(b) V= 0.06.
Fig. 3. Convergence behavior of our designed algorithm under different
values of V. Thereof, the content preference of each user is generated by the
method in Section III-A.
rithm in [18] is adopted with the difference that the cache
placement scheme is replaced by our devised method,
i.e., Algorithm 1. This is because the cache decision
procedure implemented in CawR is not applicable to our
case as stated at the end of Section VI.
Two system metrics are evaluated in this section: 1) the
convergence performance of our designed joint caching and
recommendation algorithm, and 2) the content hit ratio of
different schemes. Further, we consider different social-aware
rate thresholds, i.e., V, for each of the aforementioned metrics
since Vaffects the social neighbor set per user, which in turn
influences system’s CHR.
A. Convergence Performance
In this subsection, the convergence performance of our joint
decision algorithm is evaluated under extensive parameters
settings, as illustrated in Fig. 3 and Fig. 4. Thereof, the number
of the recommended item per subscriber is set to be R= 2. In
addition, the users preference distribution of Fig. 3 is obtained
by the manner introduced in Section III-A while that of Fig.
4 is following by (28) with win
k= 0. We use the cache hit
ratio value during the iterations to show this performance. To
be more specific, the x-axis depicts the number of iterations
while the y-axis represents the cache hit ratio of the system.
In Fig. 3(a) and Fig. 3(b), the D2D social aware rate
threshold is set to be V= 0.04 and V= 0.06, respectively.
From each of the sub-figures, we see that, our proposed algo-
rithm converges quickly under different settings. In addition,
a smaller value of cache capacity induces to a higher rate
of convergence since the size of swapping set decreases with
the decreasing of B. Besides, as expected, we see that a
large cache capacity induces to an enhanced cache efficiency.
Moreover, for any given cache capacity budget, the CHR of
the system is decreased with the increasing of V. This is due
to the fact that a large value of Vreduces the set size of the
possible content provider for each user, which in turn lower
the probability of cache hit for D2D enabled content caching
networks.
In Fig. 4, we examine how the heterogeneity of user’s
content preference impacts the convergence performance of
our designed algorithm. The extreme usage scenario where
win
k= 0 is considered, which indicates that the content
0 50 100 150
Iteration Index
8
10
12
14
16
18
Cache Hit Ratio
(a) V= 0.04.
0 50 100 150
Iteration Index
8
9
10
11
12
13
14
15
Cache Hit Ratio
(b) V= 0.06.
Fig. 4. Convergence behavior of our proposed algorithm under different
values of V, where the preference distribution per subscriber is characterized
by Zipf. Specifically, the Zipf component is set to be 0.5.
0 2 4 6 8 10 12
Cache Capacity Budget
0
5
10
15
20
Cache Hit Ratio
(a) V= 0.02 and win
k= 1.
0 2 4 6 8 10 12
Cache Capacity Budget
0
5
10
15
20
Cache Hit Ratio
(b) V= 0.03 and win
k= 1.
Fig. 5. Cache hit ratio versus cache capacity budget per user, where the
preference distribution of each user is characterized by the method in Section
III-A.
preference distributions of all users are homogeneous. Similar
conclusions as that of Fig. 3 are attained, details are not
redundantly expressed here. In addition, with the same setting
of V, the performance of our method under win
k= 0 is better
than that of the scenario where win
k= 1 because the diversities
among users are eliminated in the first case, resulting in a high
cache hit probability for our joint decision algorithm.
B. Content Hit Ratio
Fig. 5 and Fig. 6 illustrate the cache hit ratios of our
proposed algorithm as well as the extensive baselines versus
the cache capacity budget per user. Thereof, the preference
distribution parameter win
kin (28) are set to be 1 and 0,
respectively. In addition, the recommendation size is assumed
to be R= 5. We distinguish the observations from the two
figures in these following paragraphs.
First, we consider Fig. 5, in Fig. 5(a) and Fig. 5(b), V
is set to be 0.02 and 0.03, respectively. As expected, the
cache hit ratio of all the schemes increases with the increasing
of cache capacity budget. In addition, for any given V, our
designed scheme always achieves the optimal performance
as regards cache hit ratio owning to the jointly optimized
decisions. Besides, CawR is not the best, in particular when
the cache capacity budget is high. This is because without
globally optimal cache placement, the termination of CawR
after a single recommendation amendment step is not ensured,
which leaves space for further performance improvements as
shown by our iterative joint optimization algorithm. Moreover,
Baseline 2 and Baseline 4 have better performance than that
12
0 2 4 6 8 10 12
Cache Capacity Budget
5
10
15
20
Cache Hit Ratio
(a) V= 0.02 and win
k= 0.
0 2 4 6 8 10 12
Cache Capacity Budget
5
10
15
20
Cache Hit Ratio
(b) V= 0.03 and win
k= 0.
Fig. 6. Cache hit ratio versus cache capacity budget per user, where the
preference distribution of each subscriber is captured by Zipf with component
set as 1.1.
2 4 6 8 10
Cache Capacity Budget
0
0.2
0.4
0.6
0.8
1
Traffic Offloading Ratio
(a) V= 0.02 and win
k= 1.
2 4 6 8 10
Cache Capacity Budget
0
0.2
0.4
0.6
0.8
1
Traffic Offloading Ratio
(b) V= 0.03 and win
k= 1.
Fig. 7. Traffic offloading ration versus cache capacity budget per user.
of Baseline 3 since both of them adopt the top cache and top
recommendation mechanisms. Baseline 3 performs worse than
the other three recommendation-aware strategies because its
recommendation is not seize the momentum of caching policy,
restricting to fully reap the gains of caching to some extent.
Furthermore, it is worth noting that, a large value of Vreduces
the achievable cache hit values of all the strategies (except
Baseline 4) since the possible content providers of each user
are downsized. As far as Baseline 4, all the users cache the
same items and be recommended by the same contents, the
changing of Vwill not affect the content provider probabilities
of the adjacent users.
Then, we apply Fig. 6 to explore the effects of heterogeneity
among users on the cache efficiency of all six approaches, i.e.,
we set win
k= 0. It can be seen that our developed scheme
outperforms the four baselines in all simulated scenarios, as
well as the Revised CawR benchmark. It is noteworthy that
with win
k= 0, three recommendation enabled benchmarks,
i.e., Baselines 2, 3 and 4 are reduced to one policy in
accordance with their definitions. Besides, the schemes with
recommendation outperform Baseline 1, therein no recom-
mendation is conducted, demonstrating the effectiveness of
recommendation mechanism. Besides, with the increasing of
V, the cache hit ratio of our scheme decreased slightly and that
of the other strategies remain unchanged due to their working
mechanisms. Moreover, via comparing Fig. 5 to Fig. 6, we see
that under the same system parameters, our proposed algorithm
with homogenous users preference distribution achieves higher
cache hit ratio when compared with that of the heterogenous
case, which stays consistent with the foregoing analysis.
Fig. 7 plots the BS traffic offloading ratios (TOR) of differ-
2 4 6 8 10
Cache Capacity Budget
0
5
10
15
20
Cache Hit Ratio
Fig. 8. Cache hit ratio of our propose scheme versus cache capacity budget
under different recommendation threshold, Q.
ent approaches, wherein the definition of TOR is followed by
equation (22) in [7]. More specifically, we stipulate V= 0.02
and V= 0.03 for Fig. 7(a) and Fig. 7(b), respectively. In both
two figures, the x-axis and y-axis depict the cache capacity
budget per user and the value of TOR, respectively. A higher
value of TOR represents a larger number of contents that are
delivered by D2D communication, which further expresses a
reduced BS traffic load. Based on Fig. 7, we observe that
the TOR of each scheme increases with the increasing of
cache capacity budget per user. In addition, we see that the
proposed decision-making scheme induces the highest TOR.
For example, when V= 0.02 and B= 3, the TOR of our
developed optimization strategy is 70.9%,29.1%,151.0%,
431.4%, and 36.5% more than Baseline 1, Baseline 2, Baseline
3, Baseline 4, and Revised CawR, respectively, showing the
capability of our algorithm in terms of alleviating BS’s traffic
pressure. Furthermore, via comparing Fig. 7(a) with Fig. 7(b),
a larger value of Vresults in an decreased value of TOR
for each scheme. This is because, increasing Vdegrades
the capability of D2D communication between users. This
observation is consistent with the analysis in Fig. 5.
Subsequently, we investigate the effect of recommendation
quality threshold, i.e., Q, on the performance of our devised
joint optimization algorithm in terms of cache hit ratio, as
demonstrated by Fig. 8. Therein, the recommendation quantity
per user and the social-aware rate threshold are set to be R=
10 and V= 0.03, respectively. In addition, we assume win
k=
1. Note that similar trends are attainable for other parameters
settings, which are not plotted here for simplicity. From Fig. 8,
we notice that a higher value of Qinduces a reduced cache hit
ratio due to the fact that increasing the value of Qdownsizes
the total number of feasible recommendation combinations,
which can be seen from C2of P(1) as well. This, in turn,
degrades the performance of our optimization approach.
At last, we examine in Fig. 9 the effect of recommendation
size on cache efficiency among different schemes. Thereof,
the cache capacity budget per subscriber is assumed to be 2.
Specifically, in Fig. 9(a) and Fig. 9(b), we consider win
k= 1
and win
k= 0, respectively. We first focus on Fig. 9(a).
It can be seen that, our proposed scheme always has the
highest cache hit ratio among all the strategies, while the
Revised CawR is usually the second best performing strategy.
Besides, with the increasing of recommendation size, all
the recommendation-aware methods have the reduced cache
efficiency values, which is in consistent with the findings
13
234567
Recommendation Size
0
5
10
15
20
Cache Hit Ratio
(a) V= 0.02 and win
k= 1.
234567
Recommendation Size
6
8
10
12
14
16
18
20
Cache Hit Ratio
(b) V= 0.02 and win
k= 0.
Fig. 9. Cache hit ratio versus recommendation size per user.
in [17]–[19]. The reason is two-fold. On one hand, a large
number of recommendations making the preference distribu-
tion more flat, which is unprofitable to the cache efficiency’s
enhancement. On the other hand, increasing the number of the
recommended items induces boosted request probabilities for
these contents to some extent. Nevertheless, the cache size
is limited, which can not fully bear the recommendations,
resulting in a decrease cache hit probability. Moreover, it
is noticeable that the performance loss of our algorithm is
not so much remarkable with the increasing of R, since for
the proposed algorithm, the caching policy and the recom-
mendation decision are iteratively optimized. This in return
demonstrates how the recommendation and caching optimiza-
tion in the proposed scheme can be useful for improving
caching efficiency. Meanwhile, from Fig. 9(b), we see that,
all the recommendation enabled schemes outperform Baseline
1. Furthermore, when compared Fig. 9(b) with Fig. 9(a), it
is noticeable that, the homogeneous preference distribution
accompanied by an enhanced cache efficiency for Baselines
3, Baseline 4, and Revised CawR. Since Baseline 2 reduces
to be Baselines 3 and 4, its performance is decrease when each
user has homogenous preference distribution.
VIII. CONCLUSION
In this work, we examined how recommendation can be
implemented to enhance the caching efficiency of D2D en-
abled wireless content caching networks. Towards this end, a
cache hit ratio maximization problem was formulation. To be
more specific, we quantitatively characterized how cache hit
ratio can be jointly affected by recommendation and caching.
In addition, the user specific recommendation quantity, rec-
ommendation quality as well as cache capacity budget were
taken into account. We demonstrated the NP-hardness of the
maximization problem with rigourous mathematical proof.
To make the NP-hard problem tractable, we decoupled the
original problem into two subproblems, whereafter the corre-
sponding approaches were designed. Based on that, an iterative
algorithm was proposed to obtain the joint decision policies,
which had provable convergence guarantee and polynomial
time complexity. Extensive numerical results revealed the
effectiveness of our designed versatile algorithm compared to
various baselines. Notice that the successful implementation
of wireless edge caching is crucially depends on joint content
delivery, cache placement, or/and recommendation decisions,
future work will involve the joint optimization for the forego-
ing three aspects.
REF ER EN CE S
[1] Ericsson, “The Ericsson mobility report,” Nov 2019. [Online]. Available:
https://www.ericsson.com/en/mobility-report.
[2] D. Liu, B. Chen, C. Yang, and A. F. Molisch, “Caching at the
wireless edge: design aspects, challenges, and future directions,” IEEE
Communications Magazine, vol. 54, no. 9, pp. 22–28, Sep. 2016.
[3] J. Rao, H. Feng, C. Yang, Z. Chen, and B. Xia, “Clustered device-to-
device caching based on file preferences,in Proc. IEEE International
Conference on Communications (ICC), May. 2016.
[4] Z. Chen and M. Kountouris, “D2D caching vs. small cell caching:
Where to cache content in a wireless network?” in Proc. IEEE Signal
Processing Advances in Wireless Communications (SPAWC), Jul. 2016.
[5] D. Wu, L. Zhou, and Y. Cai, “Social-aware rate based content sharing
mode selection for D2D content sharing scenarios,” IEEE Transactions
on Multimedia, vol. 19, no. 11, pp. 2571–2582, Dec. 2017.
[6] B. Chen, C. Yang, and Z. Xiong, “Optimal caching and scheduling for
cache-enabled D2D communications,” IEEE Communications Letters,
vol. 21, no. 5, pp. 1155–1158, Jan. 2017.
[7] T. Zhang, X. Fang, Y. Liu, G. Y. Li, and W. Xu, “D2D-enabled
mobile user edge caching: A multi-winner auction approach,” IEEE
Transactions on Vehicular Technology, vol. 68, no. 12, pp. 12 314–
12 328, Dec 2019.
[8] T. Zhang, H. Fan, J. Loo, and D. Liu, “User preference aware caching
deployment for device-to-device caching networks,IEEE Systems Jour-
nal, vol. 13, no. 1, pp. 226–237, Mar. 2019.
[9] X. Zhang, Y. Wang, R. Sun, and D. Wang, “Clustered device-to-
device caching based on file preferences,in Proc. IEEE International
Symposium on Personal, Indoor and Mobile Radio Communications
(PIMRC), Oct. 2016.
[10] K. S. Khan, Y. Yin, and A. Jamalipour, “On the application of agglomer-
ative hierarchical clustering for cache-assisted D2D networks,in Proc.
IEEE Annual Consumer Communications & Networking Conference
(CCNC), Jan. 2019.
[11] B. Chen and C. Yang, “Caching policy for cache-enabled D2D commu-
nications by learning user preference,” IEEE Transactions on Commu-
nications, vol. 66, no. 12, pp. 6586–6601, Dec. 2018.
[12] G. S. Paschos, A. Destounis, and G. Iosifidis, “Learning to cooperate in
D2D caching networks,” in Proc. IEEE Signal Processing Advances in
Wireless Communications (SPAWC), Jul. 2019.
[13] W. Jiang, G. Feng, S. Qin, T. S. P. Yum, and G. Cao, “Multi-agent
reinforcement learning for efficient content caching in mobile D2D
networks,” IEEE Communications Magazine, vol. 18, no. 3, pp. 1610–
1622, Mar. 2019.
[14] R. Zhou, S. Khemmarat, and L. Gao, “The impact of YouTube rec-
ommendation system on video views,in Proc. 10th ACM SIGCOMM
Internet Measurement Conference (IMC), pp. 404–410, May. 2010.
[15] D. K. Krishnappa, M. Zink, C. Griwodz, and P. Halvorsen, “Cache-
centric video recommendation: An approach to improve the efficiency
of YouTube caches,ACM Transactions on Multimedia Computing,
Communications, and Applications (TOMM), vol. 11, no. 4, pp. 48:1–
48:20, Jun. 2015.
[16] C. A. Gomez-Uribe and N. Hunt, “The Netflix recommender system:
Algorithms, business value, and innovation,ACM Transactions on
Management Information Systems (TMIS), vol. 6, no. 4, pp. 1–19, Dec.
2015.
[17] L. E. Chatzieleftheriou, M. Karaliopoulos, and I. Koutsopoulos,
“Caching-aware recommendations: Nudging user preferences towards
better caching performance,” in Proc. IEEE International Conference
on Computer Communications (INFOCOM), May. 2017.
[18] ——, “Jointly optimizing content caching and recommendations in small
cell networks,” IEEE Transactions on Mobile Computing, vol. 18, no. 1,
pp. 125–138, Jan. 2019.
[19] L. E. Chatzieleftheriou, G. Darzanos, M. Karaliopoulos, and I. Kout-
sopoulos, “Joint user association, content caching and recommendations
in wireless edge networks,” ACM SIGMETRICS Performance Evaluation
Review, vol. 46, no. 3, pp. 12–17, Dec. 2018.
[20] K. Qi, B. Chen, C. Yang, and S. Han, “Optimizing caching and
recommendation towards user satisfaction,in Proc. IEEE International
Conference on Wireless Communications and Signal Processing (WC-
SP), pp. 1–7, Dec. 2018.
14
[21] D. Liu and C. Yang, “A learning-based approach to joint content
caching and recommendation at base stations,” in Proc. IEEE Global
Communications Conference (GLOBECOM), Dec. 2018.
[22] S. Kastanakis, P. Sermpezis, V. Kotronis, and X. Dimitropoulos,
“CABaRet: Leveraging recommendation systems for mobile edge
caching,” in Proc. ACM SIGCOMM workshops: Workshop on Mobile
Edge Communications, Aug. 2018.
[23] P. Sermpezis, T. Spyropoulos, L. Vigneri, and T. Giannakas, “Femto-
caching with soft cache hits: Improving performance through recom-
mendation and delivery of related content,IEEE Journal on Selected
Areas in Communications, vol. 36, no. 6, pp. 1300–1313, Jun. 2018.
[24] T. Giannakas, P. Sermpezis, and T. Spyropoulos, “Show me the cache
optimizing cache-friendly recommendations for sequential content ac-
cess,” in Proc. IEEE International Symposium on a World of Wireless
Mobile and Multimedia Networks (WoWMoM), Jun. 2018.
[25] Y. Fu, Z. Yang, T. Q. S. Quek, and H. H. Yang, “Towards cost
minimization for wireless caching networks with recommendation and
uncharted users’ feature information,” IEEE Transactions on Wireless
Communications, Aug 2020.
[26] Y. Wang, M. Ding, Z. Chen, and L. Luo, “Caching placement with
recommendation systems for cache-enabled mobile social networks,”
IEEE Communications Letters, vol. 21, no. 10, pp. 2266–2269, Oct.
2017.
[27] K. N. Doan, T. V. Nguyen, H. Shin, and T. Q. S. Quek, “Socially-aware
caching in wireless networks with random D2D communications,” IEEE
Access, vol. 7, pp. 58 394–58 406, May 2019.
[28] Y. Zhang, M. Zhang, Y. Liu, C. Tat-Seng, Y. Zhang, and S. Ma, “Task-
based recommendation on a web-scale,” in Proc. IEEE International
Conference on Big Data (Big Data), pp. 827–836, Oct. 2015.
[29] E. Bastug, M. Bennis, E. Zeydan, M. A. Kader, I. A. Karatepe, A. S.
Er, and M. Debbah, “Big data meets telcos: A proactive caching
perspective,Journal of Communications and Networks, vol. 17, no. 6,
pp. 549–557, Dec. 2015.
[30] Y. Dong, Q. Ke, Y. Cai, B. Wu, and B. Wang, “Teledata: data mining,
social network analysis and statistics analysis system based on cloud
computing in telecommunication industry,in Proceedings of the third
ACM international workshop on cloud data management, pp. 41–48,
2011.
[31] D. Wu, L. Zhou, and Y. Cai, “Social-aware rate based content sharing
mode selection for D2D content sharing scenarios,” IEEE Transactions
on Multimedia, vol. 19, no. 11, pp. 2571–2582, Dec. 2017.
[32] M. Verhoeyen, J. D. Vriendt, and D. D. Vleeschauwer, “Optimizing
for video storage networking with recommender systems,” Bell Labs
Technical Journal, vol. 16, no. 4, pp. 97–113, Mar. 2012.
[33] D. Jannach and G. Adomavicius, “Price and profit awareness in recom-
mender systems,” in Proceedings of the RecSys Workshop, Como, Italy,
August 2017.
[34] A. Vinciarelli and G. Mohammadi, “A survey of personality computing,”
IEEE Transactions on Affective Computing, vol. 5, no. 3, pp. 273–291,
May. 2014.
[35] M. R. Garey and D. S. Johnson, Computers and intractability. W. H.
Freeman New York, 2002, vol. 29.
[36] H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems. Berlin
Heidelberg: Springer-Verlag, 2004.
[37] E. Bodine-Baron, C. Lee, A. Chong, B. Hassibi, and A. Wierman, “Peer
effects and stability in matching markets,in International Symposium
on Algorithmic Game Theory, pp. 117–129, 2011.
[38] D. Gale and L. S. Shapley, “College admissions and the stability of
marriage,” The American Mathematical Monthly, vol. 69, no. 1, pp. 9–
15, 1962.
[39] H. Sasaki and M. Toda, “Two-sided matching problems with externali-
ties,” Journal of Economic Theory, vol. 70, no. 1, pp. 93–108, 1996.
[40] R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis. John
Wiley & Sons, Inc., 2010.
[41] Y. Fu, Q. Yu, T. Q. S. Quek, and W. Wen, “Revenue maximization
for content-oriented wireless caching networks (CWCNs) with repair
and recommendation considerations,” IEEE Transactions on Wireless
Communications, vol. 20, no. 1, pp. 284–298, Jan. 2021.
[42] X. Yang, Y. Fu, W. Wen, T. Q. S. Quek, and F. Song, “Mixed-timescale
caching and beamforming in content recommendation aware Fog-RAN:
A latency perspective,IEEE Transactions on Communications, 2020.
[Online]. Available: DOI:10.1109/TCOMM.2020.3044074
Yaru Fu (S’14-M’18) received her BEng (Hons.)
in Telecommunication Engineering from Northeast
Electric Power University (NEEPU), MSc (Hons.) in
Communication and Information System from Nan-
jing University of Posts and Telecommunications
(NUPT) and Ph.D in Electronic Engineering from
City University of Hong Kong (CityU) in 2011,
2014, and 2018, respectively. Then, she joined in
the Institute of Network Coding (INC), the Chinese
University of Hong Kong (CUHK) as a Post-doctoral
Research Assistant. From Sep. 2018 to Jun. 2020,
she served as a Research Fellow (Class 2) in Singapore University of Technol-
ogy and Design. From Feb. 2016 to May. 2016, she was a visiting researcher
in Telecom Paris Tech (TPT) and Laboratory of Information, Networking
and Communication Sciences (Lincs). She was also an Intern with Nokia
Bell Labs, Paris, France. Now, she is a Research Assistant Professor with
the School of Science and Technology, The Open University of Hong Kong,
China. Her research interests include intelligent wireless communications and
networking, caching and recommendation, distributed storage systems, IoT,
and URLLC.
Lou Sala¨
un received the engineering diploma and
the M.Sc. degree from Centrale-Sup´
elec, Gif-sur-
Yvette, France, in 2016, specializing in computer
system, applied mathematics, signal processing, and
telecommunications, and the Master of Research de-
gree from University of Paris-Saclay, Saclay, France,
in 2016, specializing in computer science and soft-
ware engineering. He obtained his Ph.D. degree in
2020, on resource allocation and optimization for
the non-orthogonal multiple access from T´
el´
ecom
Paris, Paris, France, jointly working with Nokia
Bell Laboratories, Nozay, France. He is currently working as a Research
Engineer at Nokia Bell Laboratories. His research interests include algorithmic
computer science, optimization, telecommunications, resource allocation, and
distributed computing.
Xiaolong Yang received his Ph.D degree in Infor-
mation and Communication Engineering from the
School of Information and Electronics, Beijing Insti-
tute of Technology in 2020. From Dec. 2018 to Dec.
2019, he served as a visiting student in Singapore
University of Technology and Design, supervised by
Prof. Tony Q. S. Quek. Now, he is an Assistant Pro-
fessor with the School of Information and Communi-
cation Engineering, Beijing Information Science and
Technology University, Beijing, China. His research
interests include intelligent wireless communications
and networks, caching, mobile edge computing, URLLC, and recommendation
system.
Wanli Wen (S’15-M’20) received the B.S. degree
from Anhui University of Finance and Economics,
Bengbu, China, in 2011, the M.S. degree in Commu-
nication and Information Systems from Hangzhou
Dianzi University, Hangzhou, China, in 2014, and
the PhD degree in Information and Communication
Engineering from Southeast University, Nanjing,
China, in 2019. Currently, he is a postdoctoral re-
search fellow in Singapore University of Technology
and Design. His research interests include mobile
edge computing, caching, federated learning, and
physical layer security.
15
Tony Q.S. Quek (S’98-M’08-SM’12-F’18) received
the B.E. and M.E. degrees in electrical and electron-
ics engineering from the Tokyo Institute of Technol-
ogy in 1998 and 2000, respectively, and the Ph.D.
degree in electrical engineering and computer sci-
ence from the Massachusetts Institute of Technology
in 2008. Currently, he is the Cheng Tsang Man Chair
Professor with Singapore University of Technology
and Design (SUTD). He also serves as the Director
of the Future Communications R&D Programme, the
Head of ISTD Pillar, and the Deputy Director of the
SUTD-ZJU IDEA. His current research topics include wireless communica-
tions and networking, network intelligence, internet-of-things, URLLC, and
big data processing.
Dr. Quek has been actively involved in organizing and chairing sessions,
and has served as a member of the Technical Program Committee as well as
symposium chairs in a number of international conferences. He is currently
serving as an Editor for the IE EE TR ANS ACT ION S ON WI REL ES S COMM U-
NI CATIO NS and an elected member of the IEEE Signal Processing Society
SPCOM Technical Committee. He was an Executive Editorial Committee
Member for the IE EE TRANSACTIONS ON WIREL ES S COMMUNICATIONS,
an Editor for the I EEE T RANSACTIONS ON COMMUNICATIONS, and an
Editor for the I EEE WIR EL ESS COMMUNICATIONS LETT ER S.
Dr. Quek was honored with the 2008 Philip Yeo Prize for Outstanding
Achievement in Research, the 2012 IEEE William R. Bennett Prize, the 2015
SUTD Outstanding Education Awards – Excellence in Research, the 2016
IEEE Signal Processing Society Young Author Best Paper Award, the 2017
CTTC Early Achievement Award, the 2017 IEEE ComSoc AP Outstanding
Paper Award, the 2020 IEEE Communications Society Young Author Best
Paper Award, the 2020 IEEE Stephen O. Rice Prize, the 2020 Nokia Visiting
Professor, and the 2016-2020 Clarivate Analytics Highly Cited Researcher.
He is a Distinguished Lecturer of the IEEE Communications Society and a
Fellow of IEEE.
... For k ∈ K and i ∈ I, let a req k,i be the request probability of user k towards content i. Following the recommendation model in [29], we have ...
... As the recommendation states of all users jointly determine the content request state of the system, the recommendation decisions of different users are no longer independent of each other, which is different from that in [29], [31], [32]. The designed SCM works in an iterative manner. ...
... The difference lies on the recommendation mechanism. More precisely, in contrast to recommend each user its top-preferred contents, BS recommends the same top-ranked items to each user based on all users aggregated preference distribution [29]. ...
Preprint
In this paper, we exploit a behavior-shaping proactive mechanism, namely, recommendation, in cache-assisted non-orthogonal multiple access (NOMA) networks, aiming at minimizing the average system's latency. Thereof, the considered latency consists of two parts, i.e., the backhaul link transmission delay and the content delivery latency. Towards this end, we first examine the expression of system latency, demonstrating how it is critically determined by content cache placement, personalized recommendation, and delivery associated NOMA user pairing and power control strategies. Thereafter, we formulate the minimization problem mathematically taking into account the cache capacity budget, the recommendation-oriented requirements, and the total transmit power constraint, which is a non-convex, multi-timescale, and mixed-integer programming problem. To facilitate the process, we put forth an entirely new paradigm named divide-and-rule. Specifically, we first solve the short-term optimization problem regarding user pairing as well as power allocation and the long-term decision-making problem with respect to recommendation and caching, respectively. On this basis, an iterative algorithm is developed to optimize all the optimization variables alternately. Particularly, for solving the short-timescale problem, graph theory enabled NOMA user grouping and efficient inter-group power control manners are invoked. Meanwhile, a dynamic programming approach and a complexity-controllable swap-then-compare method with convergence insurance are designed to derive the caching and recommendation policies, respectively. From Monte-Carlo simulation, we show the superiority of the proposed joint optimization method in terms of both system latency and cache hit ratio when compared to extensive benchmark strategies.
... Qi et al. in [20] adopted the same model. As far as device-todevice (D2D) communication assisted caching system, the cache hit ratio maximization problem is studied by [21]. Therein, the NP-hardness of the joint cache placement and recommendation decision problem was revealed. ...
... Problem (18) is a non-linear, non-convex, and integer programming problem, which lacks of modular properties and thus is challenging to solve directly. To be more specific, (18) is a non-deterministic polynomialtime (NP)-complete programming even when J k = N for k ∈ K and p n = 1 for n ∈ N , as proven in [17], [21]. Further, the difficulty of solving (18) essentially comes from the coupling of the optimization variables, i.e., the bundle state, the recommendation decision, and the caching decision. ...
... 1: Let j = 1. 2: while N ̸ = ∅ do 3:for n ∈ N do4: Calculate R k,D k,n based on(21), where D k,n = {n} for n ∈ N . Thereof, ...
Article
In this paper, we explore the interplay between personalized bundle recommendation and cache decision on the performance of wireless edge caching networks. A revenue maximization perspective is provided. To this end, we first examine the quantitative impact of bundle recommendation on the content request probability of different users. We then specify the definition of system revenue, showing its dependence on bundle recommendation and caching policies. With that, a joint bundling, caching and recommendation decision problem is formulated to maximize the achievable system revenue, taking into account the constraints of user-distinguished recommendation quality, recommendation amount, and the cache capacity budget. To solve this non-tractable optimization problem, a divide-then-conquer methodology is adopted. Specifically, we first determine the bundle state per user, on which basis we perform the joint bundle recommendation and caching decision-making, wherein several bundling strategies with different time-complexity are devised. Last but not least, we provide detailed properties analysis for our proposed bundling and joint optimization algorithms. Comprehensive numerical simulations validate the performance enhancement of the designed solutions compared to extensive conventional single-item recommendation oriented benchmarks.
... Qi et al. in [20] adopted the same model. As far as device-todevice (D2D) communication assisted caching system, the cache hit ratio maximization problem is studied by [21]. Therein, the NP-hardness of the joint cache placement and recommendation decision problem was revealed. ...
... Problem (18) is a non-linear, non-convex, and integer programming problem, which lacks of modular properties and thus is challenging to solve directly. To be more specific, (18) is a non-deterministic polynomialtime (NP)-complete programming even when J k = N for k ∈ K and p n = 1 for n ∈ N , as proven in [17], [21]. Further, the difficulty of solving (18) essentially comes from the coupling of the optimization variables, i.e., the bundle state, the recommendation decision, and the caching decision. ...
... 1: Let j = 1. 2: while N ̸ = ∅ do 3:for n ∈ N do4: Calculate R k,D k,n based on(21), where D k,n = {n} for n ∈ N . Thereof, ...
Preprint
In this paper, we explore the interplay between personalized bundle recommendation and cache decision on the performance of wireless edge caching networks. A revenue maximization perspective is provided. To this end, we first examine the quantitative impact of bundle recommendation on the content request probability of different users. We then specify the definition of system revenue, showing its dependence on bundle recommendation and caching policies. With that, a joint bundling, caching and recommendation decision problem is formulated to maximize the achievable system revenue, taking into account the constraints of user-distinguished recommendation quality, recommendation amount, and the cache capacity budget. To solve this non-tractable optimization problem, a divide-then-conquer methodology is adopted. Specifically, we first determine the bundle state per user, on which basis we perform the joint bundle recommendation and caching decision-making, wherein several bundling strategies with different time-complexity are devised. Last but not least, we provide detailed properties analysis for our proposed bundling and joint optimization algorithms. Comprehensive numerical simulations validate the performance enhancement of the designed solutions compared to extensive conventional single-item recommendation oriented benchmarks.
... In addition, the increase in the amount of data may put higher requirements on the endurance of terminal devices. New communication technologies need to support the operation of terminal devices that can support intensive calculation and data transmission [8]. In the process of continuous development of Internet technology and computer network technology, the amount of information generated in the network is also increasing. ...
Article
Full-text available
In the process of building a city, the content of the language landscape directly reflects the level of development and civilization of the city. The language landscape of each city will change with the changes in humanities and local characteristics, so the translation of the language landscape is very important. This article analyzes the language landscape of a city in detail, introduces the meaning of the language landscape in detail, and also corrects the errors in the city’s language landscape translation process, and introduces people to the language landscape. In today’s social development process, the fifth-generation communication technology has gradually developed and matured, bringing more convenience to people’s daily lives. However, the upgraded communication technology still faces the problem of processing a large amount of data, and the traditional network system may not be able to bear the current data processing pressure. The emergence of artificial intelligence technology has created opportunities for the upgrading and development of communication technology. It can process a variety of complex data information at the same time and provide help for the smooth operation of the network system. The use of this communication network can also solve the deployment problem of network nodes and improve the efficiency and quality of language landscape translation to a certain extent.
... Li et al. [13] have investigated a distributed caching mechanism to select appropriate user nodes and allocate content at selected nodes in cellular networks using D2D communications. Fu et al. [27] have studied a caching mechanism to improve the caching quality of deviceto-device facilitated mobile networks. Yang et al. [14] have presented a cost-aware energy-efficient data offloading technique to trade-off between cost, energy efficiency and delay. ...
Article
Full-text available
Caching the most likely to be requested content at the mobile devices in a cooperative manner can facilitate direct content delivery without fetching content from the remote content server and thus alleviate the user-perceived latency, reduce the burden on backhaul and minimize the duplicated content transmissions. In addition to content popularity, it is also essential to consider the users’ dynamic behaviour for real-time applications, which can further improve the communication chances between user devices, leading to efficient content service time. The majority of previous studies consider stationary network topologies, in which all users remain stationary during data transmission, and the user can receive desired content from the corresponding base station. In this work, we study an essential issue: caching content by taking advantage of user mobility and the randomness of user interaction time. In a cooperative caching problem, we consider a realistic scenario with user devices moving at various velocities. We formulate the cache placement problem as maximization of saved delay with capacity and deadline constraints by considering the contact duration and inter-contact time among the user devices. We designed on-policy learning integrated fuzzy logic-based caching scheme to solve the high dimensionality of the proposed Integer linear programming problem. The proposed caching schemes improve the long-term reward and higher convergence rate than the Q-learning mechanism. Extensive simulation results demonstrate that the proposed cooperative caching mechanism significantly improves the performance in terms of reward, acceleration ratio, hit ratio and offloading ratio compared with existing mechanisms.
... In the second step, the iterative algorithm of optimization is proposed, which achieves the best way of computational complexity and optimization. Network edge caching for D2D can reduce the burden of transmission, which is a more promising technology [5]. But it relies too much on the content preferences of individual users, so we must take some proactive measures if we want to give full play to its advantages. ...
Article
Full-text available
The deployment of cache and computing resources in 5G mobile communication networks is considered as an important way to reduce network transmission delay and redundant content transmission and improve the efficiency of content distribution and network computing processing capacity, which has been widely concerned and recognized by academia and industry. Aiming at the development trend of cache and computing resource allocation in 5G mobile communication networks, in order to improve the efficiency of content cache and reduce network energy consumption, a 5G network cache optimization strategy based on Stackelberg game was proposed, which modeled network operators and content providers as multimaster and multislave Stackelberg game model. Providers buy base station storage space from network operators to cache popular content. In this paper, we construct the strategy space and profit function of the two sides of the game and prove the existence of Nash equilibrium solution among content providers given a set of base station rental prices of network operators. In this paper, distributed iterative algorithm is used to solve the game model, and the optimal base station pricing of network operators and the optimal base station occupancy rate of content providers are obtained.
Article
Edge caching enables low-delay and high-quality data services for the Industrial Internet. However, traditional popularity-based edge caching ignores the diversity and evolution of user interest, especially among user groups, and therefore has limited quality of experience guarantees for users. In this regard, a recommendation-aided edge caching approach is proposed to leverage the time-varying user interest. Specifically, a dynamic interest capture model was proposed to mine the individual user interest, based on which, a group interest aggregation algorithm is then studied to determines the content caching strategies for edge nodes. Thereafter, an edge content recommendation is further proposed to optimizes the cache hit ratio while ensuring a satisfying recommendation hit ratio based on the personalized user interest and given caching decision. The effectiveness of the proposed approach is finally validated by comparing with other baseline approaches.
Article
In this paper, we propose a joint spectrum and power optimisation (SPO) for multi-hop multi-path (MHMP) device-to-device (D2D) video delivery in beyond 5G (B5G/6G) networks, where the system resources such as spectrum, energy, storage, and content of mobile users (MUs), are taken into account. Particularly, the downlink spectrum resources of the sharing users (SUs) are reused by the transmitters (TXs) of D2D hops and the energy resources of the TXs are utilised for D2D communications. We further exploit the videos stored in the caching users (CUs) located more than one D2D hop far away from the requesting users (RUs) to establish MHMP D2D video delivery sessions from the CUs to the RUs. Then, the SPO problem is formulated for the optimal spectrum sharing pairs of SUs and TXs and the optimal transmission powers allocated to the TXs. Genetic algorithms (GAs) are developed to solve the SPO problem with respect to both binary variable (spectrum sharing) and real variable (power allocation). The SPO solution allows the RUs to alternately request the videos not only from the macro base station over conventional cellular networks but also from the CUs over MHMP D2D communications at the highest quality of service, i.e., maximum video delivery capacity and low power consumption. Simulation results are analysed to demonstrate the feasibility of GAs and the benefits of the proposed SPO solution in comparison with other conventional schemes.
Article
Full-text available
Content caching is recognized as a promising solution to release the heavy burden of backhaul links and decrease the content transmission latency in Fog radio access networks (Fog-RANs). However, the content caching design is still a challenging problem with considering the user request patterns, the content delivery strategies, and the limited caching capacity. Recommendation has the capability of reshaping users' content requests for further prompting caching gain. The joint recommendation , caching, beamforming holds the potential to improve the system performance of Fog-RANs. In this paper, a joint recommendation , caching, and beamforming scheme is proposed for multi-cell multi-antenna recommendation aware Fog-RANs. Aiming at minimizing the content transmission latency, we formulate a joint recommendation, caching, and beamforming optimization problem. The minimization problem is a very challenging two-timescale mixed integer nonlinear programming problem, which is hard to solve in general. By exploring structural properties of the problem, we propose an alternative optimization algorithm with low complexity through decomposing the original problem into three sub-problems. Extensive simulations show that our proposed method can significantly reduce the content transmission delay.
Article
Full-text available
In this paper, we investigate the performance gains that are achievable when jointly controlling (i) in which Small-cell Base Stations (SBSs) mobile users are associated to, (ii) which content items are stored at SBS co-located caches and (iii) which content items are recommended to the mobile users who are associated to different SBSs. We first establish a framework for the joint user association, content caching and recommendations problem, by specifying a set of necessary conditions for all three component functions of the system. Then, we provide a concrete formulation of the joint problem when the objective is to maximize the total hit ratio over all caches. We analyze the problems that emerge as special cases of the joint problem, when one of the three functions is carried out independently, and use them to characterize its complexity. Finally, we propose a heuristic that tackles the joint problem. Proof-of-concept simulations demonstrate that even this simple heuristic outperforms an optimal algorithm that takes only caching and recommendation decisions into account and provide evidence of the achievable performance gains when decisions over all three functions are jointly optimized.
Article
Caching popular contents at the network edge has been considered as a promising enabler to relieve the pressure on networks due to the fact that a substantial portion of global data traffic is repeatedly requested by many subscribers and thus redundantly generated. Recommendation, on the other hand, has attracted spiraling attention for its capability of reshaping users' contents demand patterns. In this paper, we examine the practicability of recommendation in boosting the gains of edge caching with uncharted users' feature information. To this end, we first characterize the average system cost for a generic network model, disclosing its dependence on the recommendation and caching strategies. Then, we formulate the joint caching and recommendation decision oriented cost minimization problem, taking the constraints on each content provider's cache capacity budget, each individual user's recommendation size and recommendation quality into account. However, the implicit information regarding users' preference makes the problem inextricable. To address this issue, a versatile long short term memory (LSTM) network assisted prediction paradigm is proposed to attain the preference schema of users with the assistance of their historical behavior data. Based on that, we rigorously prove the NP-hardness of obtaining the optimal recommendation and caching policies that jointly minimize the system cost. Therewith, an iterative sub-optimal algorithm is developed, which has provable polynomial time complexity and convergence guarantee. Extensive simulation results validate the effectiveness of our proposed LSTM enabled feature information prediction approach and the convergence performance of the devised joint decision making methodology. In addition, it is shown that the proposed scheme outperforms numerous benchmarks significantly.
Article
To maintain reliability of content-oriented wireless caching networks (CWCNs), repair mechanism is of necessity to be considered due to the natural that storage entities are individually unreliable and thus subject to failure on account of hardware error, network congestion or software updating. Meanwhile , recommendation is tunable for edge caching performance improvement. In this paper, we study the revenue maximization problem for CWCNs with both repair and recommendation considerations. The formulated problem is an integer non-convex and non-linear problem, and thus is difficult to be solved. The difficulties are intrinsically derived from the implicit weighted sum costs (WSCs) as regards storage and repair of each content and the coupling among the Boolean variables. For the sake of analytical tractability, a two-step methodology is developed. Specifically, we first explore the optimal storage and repair amount among the content providers to minimize the WSCs in terms of successfully fixing any occurred data corruption for the stored contents. Thereof, an explicit instance is provided to show how the contents can be coded, stored and then repaired in our network given that an error occurs. Based on the obtained storage and repair amount vectors, we solve the resultant joint caching and recommendation decision making problem (DMP). To be more specific, we decouple the DMP into a pair of subproblems, namely a cache placement and a recommendation optimization subproblems. For each subproblem, a globally optimal and a time-efficient suboptimal solutions are developed, respectively. Later, a versatile iterative paradigm is devised to do the decision making jointly. The convergence performance and the complexity analysis of the proposed algorithms are rigorously analyzed. Numerical results confirm the convergence performance of our iterative algorithms and illustrate their revenue improvements compared to various baseline schemes.
Article
In device-to-device (D2D)-enabled caching cellular networks, the user terminals (UTs) collaboratively store and share a large volume of popular contents from the base station (BS) for traffic offloading and delivery delay reduction. In this article, the multi-winner auction based caching placement in D2D-enabled caching cellular networks is investigated for UT edge caching incentive and content caching redundancy reduction. Firstly, a multi-winner once auction for UT edge caching is modeled which auctions multiple contents for multiple UTs. Then the optimization problem for content caching revenue maximization is formulated. Specifically, the “cache conflict” restriction relationship among UTs is used as one of the constraints in the problem to reduce the content caching redundancy in a UT movement scenario. The problem is solved by semidefinite programming (SDP) relaxation to obtain an approximate optimal caching placement. Moreover, the payment strategy of the auction is developed as a Nash bargaining game for personal profit fairness among the UTs who win the auction for content caching. Subsequently, a multi-winner once auction based caching (MOAC) placement algorithm is proposed. In addition, due to the high complexity of MOAC, we further propose a heuristic multi-winner repeated auction based caching placement (MRAC) algorithm, which can greatly reduce the complexity with only tiny performance loss. Simulation results show that the proposed algorithms can reduce the traffic load and average content access delay effectively compared with the existing caching placement algorithms.
Article
Pushing contents to users with device-to-device (D2D) data sharing is considered as a promising solution to overcome backhaul congestion. However, this model is associated with critical issues which are user selfishness in terms of sharing personal resources and security concern when connecting with strange devices. Therefore, we propose in this work the notion of random D2D connection where the probabilities that devices are connected for receiving or sharing data are manipulated by users themselves. Moreover, these probability values can also be treated as variables to be optimized. Based on that, we address the backhaul congestion issue and formulate it as a non-convex optimization problem. Two solving schemes are proposed based on primal decomposition and alternating direction method of multipliers algorithm, respectively. In addition, these methods are designed in both centralized and distributed manners. Besides that, the congestion probability expression are derived in the special case giving an upper bound for the performance of our presented solution. Numerical results are provided to illustrate the effectiveness of the proposed method.
Conference Paper
With rapid increase in the use of traffic-intensive applications, approaches that improve users experience by reducing delay are recently receiving enormous attention. Caching in Device-to-Device (D2D) networks, in particular, is considered as an effective technique to improve the service quality of the network. In this paper, an agglomerative hierarchical clustering algorithm is proposed for a cache-assisted D2D communication network. The algorithm considers users preferences and groups them into the same cluster based on the similarity of their requested content. An optimal caching strategy has been applied and the cache hit probability has further being optimized within each cluster. Performance of the algorithm has been examined in different clusters, considering both sparse and dense user environments. Simulation results show that the cache hit probability within each cluster is higher for higher Zipf parameter, denser domains, and larger number of participating devices. The D2D cache hit probability has also been examined with changing number of clusters under a base station. In this scenario, the results show that the clustering based D2D cache hit probability is higher than the non-clustered case, and the cache hit probability increases with increasing number of clusters.
Article
To address the increase of multimedia traffic dominated by streaming videos, user equipment (UE) can collaboratively cache and share contents to alleviate the burden of base-stations. Prior work on D2D caching policies assumes perfect knowledge of the content popularity distribution. Since the content popularity distribution is usually unavailable in advance, a machine learning based caching strategy that exploits the knowledge of content demand history would be highly promising. Thus, we design D2D caching strategies using multi-agent reinforcement learning in this paper. Specifically, we model the D2D caching problem as a multi-agent multi-armed bandit problem, and use Q-learning to learn how to coordinate the caching decisions. UEs can be independent learners (ILs) if they learn the Qvalues of their own actions, and joint action learners (JALs) if they learn the Q-values of their own actions in conjunction with those of other UEs. As the action space is very large leading to high computational complexity, a modified combinatorial upper confidence bound algorithm is proposed to reduce the action space for both IL and JAL. Simulation results show that the proposed JAL-based caching scheme outperforms IL-based caching scheme and other popular caching schemes in terms of average downloading latency and cache hit rate.