AdCell: Ad Allocation in Cellular Networks

Abstract

With more than four billion usage of cellular phones worldwide, mobile
advertising has become an attractive alternative to online advertisements. In
this paper, we propose a new targeted advertising policy for Wireless Service
Providers (WSPs) via SMS or MMS- namely {\em AdCell}. In our model, a WSP
charges the advertisers for showing their ads. Each advertiser has a valuation
for specific types of customers in various times and locations and has a limit
on the maximum available budget. Each query is in the form of time and location
and is associated with one individual customer. In order to achieve a
non-intrusive delivery, only a limited number of ads can be sent to each
customer. Recently, new services have been introduced that offer location-based
advertising over cellular network that fit in our model (e.g., ShopAlerts by
AT&T) .
We consider both online and offline version of the AdCell problem and develop
approximation algorithms with constant competitive ratio. For the online
version, we assume that the appearances of the queries follow a stochastic
distribution and thus consider a Bayesian setting. Furthermore, queries may
come from different distributions on different times. This model generalizes
several previous advertising models such as online secretary problem
\cite{HKP04}, online bipartite matching \cite{KVV90,FMMM09} and AdWords
\cite{saberi05}. ...

Full text

Page 1

AdCell: Ad Allocation in Cellular Networks
Saeed Alaei‡1, Mohammad T. Hajiaghayi§12, Vahid Liaghat¶1,
Dan Pei2, and Barna Saha?1
{saeed, hajiagha, vliaghat, barna}@cs.umd.edu,
peidan@research.att.com
1University of Maryland, College Park, MD, 20742
2AT&T Labs - Research, 180 Park Avenue, Florham Park, NJ 07932
Abstract. With more than four billion usage of cellular phones worldwide, mo-
bile advertising has become an attractive alternative to online advertisements.
In this paper, we propose a new targeted advertising policy for Wireless Ser-
vice Providers (WSPs) via SMS or MMS- namely AdCell. In our model, a WSP
charges the advertisers for showing their ads. Each advertiser has a valuation for
specific types of customers in various times and locations and has a limit on the
maximum available budget. Each query is in the form of time and location and is
associated with one individual customer. In order to achieve a non-intrusive de-
livery, only a limited number of ads can be sent to each customer. Recently, new
services have been introduced that offer location-based advertising over cellular
network that fit in our model (e.g., ShopAlerts by AT&T) .
We consider both online and offline version of the AdCell problem and develop
approximation algorithms with constant competitive ratio. For the online version,
we assume that the appearances of the queries follow a stochastic distribution
and thus consider a Bayesian setting. Furthermore, queries may come from dif-
ferent distributions on different times. This model generalizes several previous
advertising models such as online secretary problem [10], online bipartite match-
ing [13,7] and AdWords [18]. Since our problem generalizes the well-known sec-
retary problem, no non-trivial approximation can be guaranteed in the online set-
ting without stochastic assumptions. We propose an online algorithm that is sim-
ple, intuitive and easily implementable in practice. It is based on pre-computing
a fractional solution for the expected scenario and relies on a novel use of dy-
namic programming to compute the conditional expectations. We give tight lower
bounds on the approximability of some variants of the problem as well. In the of-
flinesetting,wherefull-informationisavailable,weachievenear-optimalbounds,
matching the integrality gap of the considered linear program. We believe that our
proposed solutions can be used for other advertising settings where personalized
advertisement is critical.
Keywords: Mobile Advertisement, AdCell, Online, Matching
‡Supported in part by NSF Grant CCF-0728839.
§Supported in part by NSF CAREER Award, ONR Young Investigator Award, and Google
Faculty Research Award.
¶Supported in part by NSF CAREER Award, ONR Young Investigator Award, and Google
Faculty Research Award.
?Supported in part by NSF Award CCF-0728839, NSF Award CCF-0937865.

Page 2

2 S. Alaei, M.T. Hajiaghayi, V. Liaghat, D. Pei and B. Saha
1 Introduction
In this paper, we propose a new mobile advertising concept called Adcell. More than
4 billion cellular phones are in use world-wide, and with the increasing popularity of
smart phones, mobile advertising holds the prospect of significant growth in the near fu-
ture. Some research firms [1] estimate mobile advertisements to reach a business worth
over 10 billion US dollars by 2012. Given the built-in advertisement solutions from
popular smart phone OSes, such as iAds for Apple’s iOS, mobile advertising market is
poised with even faster growth.
In the mobile advertising ecosystem, wireless service providers (WSPs) render the
physical delivery infrastructure, but so far WSPs have been more or less left out from
profiting via mobile advertising because of several challenges. First, unlike web, search,
application, and game providers, WSPs typically do not have users’ application context,
which makes it difficult to provide targeted advertisements. Deep Packet Inspection
(DPI) techniques that examine packet traces in order to understand application context,
is often not an option because of privacy and legislation issues (i.e., Federal Wiretap
Act). Therefore, a targeted advertising solution for WSPs need to utilize only the infor-
mation it is allowed to collect by government and by customers via opt-in mechanisms.
Second, without the luxury of application context, targeted ads from WSPs require non-
intrusive delivery methods. While users are familiar with other ad forms such as ban-
ner, search, in-application, and in-game, push ads with no application context (e.g., via
SMS) can be intrusive and annoying if not done carefully. The number and frequency
of ads both need to be well-controlled. Third, targeted ads from WSPs should be well
personalized such that the users have incentive to read the advertisements and take pur-
chasing actions, especially given the requirement that the number of ads that can be
shown to a customer is limited.
In this paper, we propose a new mobile targeted advertising strategy, AdCell, for
WSPs that deals with the above challenges. It takes advantage of the detailed real-time
location information of users. Location can be tracked upon users’ consent. This is al-
ready being done in some services offered by WSPs, such as Sprint’s Family Location
and AT&T’s Family Map, thus there is no associated privacy or legal complications. To
locate a cellular phone, it must emit a roaming signal to contact some nearby antenna
tower, but the process does not require an active call. GSM localization is then done by
multi-lateration3based on the signal strength to nearby antenna masts [22]. Location-
based advertisement is not completely new. Foursquare mobile application allows users
to explicitly ”check in” at places such as bars and restaurants, and the shops can ad-
vertise accordingly. Similarly there are also automatic proximity-based advertisements
using GPS or bluetooth. For example, some GPS models from Garmin display ads for
the nearby business based on the GPS locations [23]. ShopAlerts by AT&T4is another
application along the same line. On the advertiser side, popular stores such as Starbucks
are reported to have attracted significant footfalls via mobile coupons.
3The process of locating an object by accurately computing the time difference of arrival of a
signal emitted from that object to three or more receivers.
4http://shopalerts.att.com/sho/att/index.html?ref=portal

Page 3

AdCell: Ad Allocation in Cellular Networks3
Most of the existing mobile advertising models are On-Demand, however, AdCell
sends the ads via SMS, MMS, or similar methods without any prior notice. Thus to deal
with the non-intrusive delivery challenge, we propose user subscription to advertising
services that deliver only a fixed number of ads per month to its subscribers (as it is the
case in AT&T ShopAlerts). The constraint of delivering limited number of ads to each
customer adds the main algorithmic challenge in the AdCell model (details in Section
1.1). In order to overcome the incentive challenge, the WSP can “pay” users to read
ads and purchase based on them through a reward program in the form of credit for
monthly wireless bill. To begin with, both customers and advertisers should sign-up for
the AdCell-service provided by the WSP (e.g., currently there are 9 chain-companies
participating in ShopAlerts). Customers enrolled for the service should sign an agree-
ment that their location information will be tracked; but solely for the advertisement
purpose. Advertisers (e.g., stores) provide their advertisements and a maximum charge-
able budget to the WSP. The WSP selects proper ads (these, for example, may depend
on time and distance of a customer from a store) and sends them (via SMS) to the cus-
tomers. The WSP charges the advertisers for showing their ads and also for successful
ads. An ad is deemed successful if a customer visits the advertised store. Depending on
the service plan, customers are entitled to receive different number of advertisements
per month. Several logistics need to be employed to improve AdCell experience and
enthuse customers into participation. We provide more details about these logistics in
the full paper.
1.1AdCell Model & Problem Formulation
In the AdCell model, advertisers bid for individual customers based on their location
and time. The triple (k,?,t) where k is a customer, ? is a neighborhood (location) and
t is a time forms a query and there is a bid amount (possibly zero) associated with
each query for each advertiser. This definition of query allows advertisers to customize
their bids based on customers, neighborhoods and time. We assume a customer can
only be in one neighborhood at any particular time and thus at any time t and for each
customer k, the queries (k,?1,t) and (k,?2,t) are mutually exclusive, for all distinct
l1,l2. Neighborhoods are places of interest such as shopping malls, airports, etc. We
assume that queries are generated at certain times (e.g., every half hour) and only if a
customer stays within a neighborhood for a specified minimum amount of time. The
formal problem definition of AdCell Allocation is as follows:
AdCell Allocation There are m advertisers, n queries and s customers. Advertiser i
has a total budget biand bids uijfor each query j. Furthermore, for each customer k ∈
[s], let Skdenote the queries corresponding to customer k and ckdenote the maximum
number of ads which can be sent to customer k. The capacity ckis associated with
customer k and is dictated by the AdCell plan the customer has signed up for. Advertiser
i pays uijif his advertisement is shown for query j and if his budget is not exceeded.
That is, if xijis an indicator variable set to 1, when advertisement for advertiser i is
shown on query j, then advertiser i pays a total amount of min(?
total payment?
jxijuij,bi). The
goal of AdCell Allocation is to specify an advertisement allocation plan such that the
imin(?
jxijuij,bi) is maximized.

Page 4

4 S. Alaei, M.T. Hajiaghayi, V. Liaghat, D. Pei and B. Saha
The AdCell problem is a generalization of the budgeted AdWords allocation prob-
lem [4,21] with capacity constraint on each customer and thus is NP-hard. Along with
the offline version of the problem, we also consider its online version where queries
arrive online and a decision to assign a query to an advertiser has to be done right away.
With arbitrary queries/bids and optimizing for the worst case, one cannot obtain any
approximation algorithm with ratio better than
that online AdCell problem also generalizes the secretary problem for which no deter-
ministic or randomized online algorithm can get approximation ratio better than1
the worst case.5. Therefore, we consider a stochastic setting.
For the online AdCell problem, we assume that each query j arrives with proba-
bility pj. Upon arrival, each query has to be either allocated or discarded right away.
We note that each query encodes a customer id, a location id and a time stamp. Also
associated with each query, there is a probability, and a vector consisting of the bids for
all advertisers for that query. Furthermore, we assume that all queries with different ar-
rival times or from different customers are independent, however queries from the same
customer with the same arrival time are mutually exclusive (i.e., a customer cannot be
in multiple locations at the same time).
1
n. This follows from the observation
nin
1.2 Our Results and Techniques
Here we provide a summary of our results and techniques. We consider both the offline
and online version of the problem. In the offline version, we assume that we know ex-
actly which queries arrive. In the online version, we only know the arrival probabilities
of queries (i.e., p1,··· ,pm).
We can write the AdCell problem as the following random integer program in which
Ijis the indicator random variable which is 1 if query j arrives and 0 otherwise:
?
∀j ∈ [n] :
i
?
Xij∈ {0,1}
We will refer to the variant of the problem explained above as IPBC. We also consider
variants in which there are either budget constraints or capacity constraints but not both.
We refer to these variants as IPBand IPCrespectively. The above integer program can
be relaxed to obtain a linear program LPBC, where we maximize?
refer to by (B). We relax Xij∈ {0,1} to Xij∈ [0,1]. We also refer to the variant of
5The reduction of the secretary problem to AdCell problem is as follows: consider a single
advertiser with large enough budget and a single customer with a capacity of 1. The queries
correspond to secretaries and the bids correspond to the values of the secretaries. So we can
only allocate one query to the advertiser.
maximize.
i
min(
?
j
Xijuij,bi)
(IPBC)
?
Xij≤ Ij
?
(F)
∀k ∈ [s] :
j∈Sk
i
Xij≤ ck
(C)
i
?
jXijuijwith
the constraints (F), (C) and additional budget constraint?
jXijuij ≤ biwhich we

Page 5

AdCell: Ad Allocation in Cellular Networks5
this linear program with only either constraints of type (B) or constraints of type (C)
as LPBand LPC.
In the offline version, for all i ∈ [m] and j ∈ [n], the values of Ijare precisely
known. For the online version, we assume to know the E[Ij] in advance and we learn
the actual value of Ijonline. We note a crucial difference between our model and the
i.i.d model. In i.i.d model the probability of the arrival of a query is independent of the
time, i.e., queries arrive from the same distribution on each time. However, in AdCell
model a query encodes time (in addition to location and customer id), hence we may
have a different distribution on each time. This implies a prophet inequality setting in
which on each time, an onlooker has to decide according to a given value where this
value may come from a different distribution on different times (e.g. see [14,11]).
A summary of our results are shown in Table 1. In the online version, we compare
the expected revenue of our solution with the expected revenue of the optimal offline
algorithm. We should emphasis that we make no assumptions about bid to budget ratios
(e.g., bids could be as large as budgets). In the offline version, our result matches the
known bounds on the integrality gap.
We now briefly describe our main techniques.
Breaking into smaller sub-problems that can be optimally solved using conditional
expectation. Theoretically, ignoring the computational issues, any online stochastic op-
timization problem can be solved optimally using conditional expectation as follows: At
any time a decision needs to be made, compute the total expected objective conditioned
on each possible decision, then chose the one with the highest total expectation. These
conditional expectations can be computed by backward induction, possibly using a dy-
namic program. However for most problems, including the AdCell problem, the size of
this dynamic program is exponential which makes it impractical. We avoid this issue by
using a randomized strategy to break the problem into smaller subproblems such that
each subproblem can be solved by a quadratic dynamic program.
Using an LP to analyze the performance of an optimal online algorithm against
an optimal offline fractional solution. Note that we compare the expected objective
value of our algorithm against the expected objective value of the optimal offline frac-
tional solution. Therefore for each subproblem, even though we use an optimal online
algorithm, we still need to compare its expected objective value against the expected
objective value of the optimal offline solution for that subproblem. Basically, we need
to compare the expected objective of an stochastic online algorithm, which works by
Offline Version
– A3
Online Version
– A?1
only budget constraints.
4-approximation algorithm.
– A
4−?
4-approximation algorithm when
∀imaxjuij ≤ ?bi.
2−1
e
?-approximation algorithm.
– A?1 −1
– A
capacity constraints.
e
?-approximation algorithm with
2-approximation algorithm with only
1
Table 1. Summary of Our Results