A Near Optimal Localized Heuristic for Voice Multicasting over Ad Hoc Wireless Networks

Abstract

Providing real-time voice multicasting over multi-hop ad hoc wireless networks is a challenging task. The unique characteristics of voice traffic (viz. small packet size, high packet rate, and soft real-time nature) make conventional multicasting protocols perform quite poorly, hence warranting application centric approaches in order to provide robustness against packet losses and lower the overhead due to high packet rate. In this paper, we first show that the optimal voice multicasting tree (OVMT) problem is NP-complete and then propose a localized distributed heuristic for minimum number of transmissions (LDMT). By incorporating LDMT in ADMR protocol, extensive simulations are done in NS-2 framework to measure the performance of LDMT for voice applications. We observed that LDMT reduces the redundant transmissions in transmitting voice packets from the source to all multicast receivers (thus reducing the overall voice traffic considerably), thereby making it suitable for voice multicasting in AWNs.

Full text

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A Near Optimal Localized Heuristic for Voice
Multicasting over Ad hoc Wireless Networks?
G. Venkat Rajua, T. Bheemarjuna Reddyb, and C. Siva Ram Murthyb
aYahoo! Software Development India Pvt. Ltd., Bangalore, India 560001
bDepartment of Computer Science and Engineering, Indian Institute of Technology Madras, India 600036
gvraju@yahoo-inc.com, arjun@cs.iitm.ernet.in, murthy@iitm.ac.in
Abstract—Providing real-time voice multicasting over multi-
hop ad hoc wireless networks is a challenging task. The unique
characteristics of voice traffic (viz. small packet size, high packet
rate, and soft real-time nature) make conventional multicasting
protocols perform quite poorly, hence warranting application
centric approaches in order to provide robustness against packet
losses and lower the overhead due to high packet rate. In this
paper, we first show that the Optimal Voice Multicasting Tree
(OVMT) problem is NP-complete and then propose a Localized
Distributed heuristic for Minimum number of Transmissions
(LDMT). By incorporating LDMT in ADMR protocol, exten-
sive simulations are done in NS-2 framework to measure the
performance of LDMT for voice applications. We observed that
LDMT reduces the redundant transmissions in transmitting voice
packets from the source to all multicast receivers (thus reducing
the overall voice traffic considerably), thereby making it suitable
for voice multicasting in AWNs.
I. INTRODUCTION
An Ad hoc Wireless Network (AWN) is a collection of mo-
bile nodes that dynamically form a temporary network without
any pre-existing infrastructure. AWNs are characterized by
high bit error rates and path breaks due to frequently changing
network topology. As developments in AWNs continue, there
is an increasing expectation of sending multimedia data to
more than one receiver simultaneously. In this paper, we
concentrate on voice multicasting as it is a key application
in many group-oriented scenarios.
Voice application can tolerate packet losses up to 5% [1],
but is highly delay sensitive (typically for interactive voice ap-
plication, the end-to-end delay should be less than 200 ms [2]).
All lately arrived packets are assumed to be lost. The unique
characteristics of voice traffic, such as small packet size, high
packet rate (typically 50 pkts/s to 100 pkts/s), and soft real-
time nature make voice multicasting a very challenging issue
in AWNs. The efficiency of AWNs for voice applications is
poor due to small voice payloads (typically 20 bytes) and large
packetization and synchronization overheads that are unique
to wireless networks [3]. Thus, to make voice multicasting
feasible in AWNs, the overall voice traffic (the total number of
voice packets exchanged in the network due to voice multicast)
must be minimized while reducing the end-to-end delay to
the maximum possible extent. An important parameter in this
connection is the Number of Forwarding Nodes (NFNs) in
the multicast tree. We define forwarding nodes as those nodes
which are not leaf nodes in the multicast tree. Note that a
forwarding node can be a receiver or a non receiver. The term
NFNs also specifies the total number of transmissions required
?This work was supported by the Microsoft Research University Relations
India.
to send a data packet to all the receivers in the multicast tree in
AWNs. Fig. 1(b) shows a multicast tree in which we mark the
forwarding nodes with double circles. In an ideal multicasting
tree structure, the NFNs must be minimum. This reduces the
overall network traffic and improves the throughput, making
it feasible to send more number of voice packets per second.
However, finding a tree with minimum NFNs is a difficult task
in AWNs as we explain further.
Recently a multicast routing protocol, Adaptive Demand-
Driven Multicast Routing protocol (ADMR) [4] was pro-
posed for efficient multicast data packet delivery in AWNs.
ADMR has the lowest normalized packet overhead (NPO,
see Section IV-A for definition) compared to other multicast
protocols, like ODMRP [6]. Basing on ADMR and exploiting
the error resilient properties of Multiple Description Coding
(MDC) and path diversity, a multiple tree video multicasting
protocol, Robust Demand-driven Video Multicast Routing
(RDVMR) protocol was proposed in [5]. RDVMR protocol
uses a novel path based Steiner tree heuristic to reduce the
number of forwarders in each tree, and constructs multiple
(k) trees in parallel with reduced number of common nodes.
Therefore, each receiver has k maximally node disjoint paths
to the source, along which different MDC descriptions are
sent. However, under high packet rates (as we show later in
Section IV-A) the RDVMR protocol fails to perform well due
to its large overhead and thus limiting its application for voice
multicasting.
The problem of finding a minimum cost multicast tree is
well known as Steiner Minimal Tree (SMT) problem. For an
excellent survey on SMT refer [7], [8]. Karp [9] demonstrated
that this problem is NP-complete even when every link has
the same cost, by a transformation from the exact cover by
3-sets. There are some heuristic algorithms to compute SMT.
For instance, the algorithm in [10] provides a 2-approximation,
and Zelikovsky [11] proposed an algorithm which obtains a
11/6-approximation. These solutions are centralized, meaning
the multicast source node needs the entire network topology
information. Mobility of nodes, or changes in their activity
status (from active to passive and vice-versa) may cause
changes in any SMT based structure. Therefore, topology
changes must be propagated to the multicast source for any
centralized solution. This may result in extreme and unac-
ceptable communication overhead in the case of AWNs. The
distributed algorithms given in [12] have very high message
passing overhead, take a long time to converge, and need to use
beaconing for neighbor discovery. Hence, most of the existing
protocols in AWNs use Shortest Path Trees (SPTs), which can
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Figure 1.
source node and A, B, C, and D are receiver nodes. The number of non-leaf nodes in (b), (c), and (d) are 4, 4, and 3, respectively. Each arc indicates one
transmission in the multicast tree and all forwarding nodes in the multicast trees are represented by double circles.
Multicast Trees (a) Original graph (b) Multicast tree generated by SPT heuristic (c) Steiner minimal tree (d) Optimal voice multicast tree; S is the
be computed in polynomial time. Lim and Kim [13] analyzed
the problem of minimal multicast trees in AWNs, but they
defined several heuristics based on the Minimal Connected
Dominating Set (MCDS) which are only valid for flooding. In
AWNs, when a node ‘A’ transmits a packet, all its neighbors
that are within the transmission range of ‘A’ can receive the
packet due to the broadcasting nature of the medium, i.e., with
a single transmission all neighbors of node ‘A’ can receive
the data. This is known as Wireless Multicast Advantage
(WMA). Given the broadcasting nature of AWNs, an SMT
does not minimize the cost (defined in terms of NFNs) of the
multicast tree (see Fig. 1(c)). The cost assignment function
used in wired networks is not well-defined for AWNs. That
is, by assigning a cost to each link of the graph, existing
formulations have implicitly assumed that a given node v
needs k transmissions to send a multicast data packet to k
of its neighbors. Thus, SMT tries to reduce the overall link
cost or node cost or both in the network which is not optimal
for AWNs. In this paper we show that the SMT does not
generally give an optimal solution. We then formulate the
problem of Optimal Voice Multicast Tree (OVMT) problem
that contains the minimum number of non-leaf nodes in the
multicast tree. We show that the OVMT problem is NP-
complete. We then propose a localized distributed heuristic
for Minimum number of Transmissions (LDMT) that achieves
superior performance compared to the related approaches in
terms of voice frame delivery ratio, NPO, and perceived voice
quality. The rest of the paper is organized as follows: Section II
discusses the OVMT problem and its NP-completeness. We
describe the proposed LDMT heuristic algorithm in detail in
Section III. In Section IV, we evaluate the performance of
LDMT heuristic algorithm through simulations and compare
with related protocols. Finally, in Section V we conclude with
possible future work.
II. OPTIMAL VOICE MULTICASTING TREE IN AWNS
A. Graph Model
An AWN can be modeled by an undirected graph,
=(V,E) where V represents the set of mobile nodes
and E represents the set of edges in the network. An edge
between two nodes v1, v2 ∈ V exists iff dist(v1,v2) ≤ r
(i.e., v1, v2 are within the communication range r). We
assume that all links are bidirectional, i.e. if node vi can
G
communicate with vj, then vjcan also communicate with vi.
Definition
∈ V , and receiver set R ⊆ V; R = {r1, r2, ···, ri;
1 ≤ i ≤ M}, where M is the number of receivers, a tree T is
said to be a multicast tree iff T has {s} ∪R ⊆ V (T) where
s and V (T) are root and vertices of tree T, respectively;
V (T) ⊆ V (G).
B. Optimal Voice Multicast Tree Problem
Given a graph G = (V,E), source node s
Given a graph G = (V,E), source node s ∈ V , and receiver
set R ⊆ V ; R = {r1, r2, ···, ri; 1 ≤ i ≤ M }, where M is the
number of receivers, the OVMT, T∗is defined as, among all
multicast trees of G, denoted by T1,T2,T3,···,Tk; for some
integer k, the number of non-leaf nodes in T∗is minimum i.e.,
if l1,l2,l3,···,lj, are leaf nodes of T∗; 2 ≤ j ≤ M, then
| V (T∗) − {l1,l2,l3,···,lj} | must be minimum compared
to all other multicast trees of G. Note that T∗need not be
unique. We call the problem of finding OVMT as optimal
voice multicast tree problem.
C. Properties of the Optimal Voice Multicast Tree
As observed in Figure 1(d), the number of non-leaf nodes
in the OVMT is minimum; which implies that the number
of transmissions in the multicast tree is also minimum. Note
that unlike SMT, OVMT is not optimal in terms of total
number of nodes or links (actually radio links in an AWN)
present in the multicast tree. OVMT improves the throughput
by minimizing the total number of transmissions required
for sending voice packets from the source to all multicast
receivers making it highly suitable for high packet rate voice
multicasting in AWNs. Each reduction in NFNs results in
large number of transmission savings. To understand this
fully, consider the following example. Suppose that in a
typical voice multicast application the source sends around
15,000 voice packets to all its multicast receivers, i.e., at each
hop these 15,000 packets are to be forwarded (transmitted).
If the NFNs is less by one, it means we can save 15,000
transmissions in the network which reduces the overall
voice traffic in the network considerably and improves the
throughput significantly. This also avoids unnecessary energy
depletion of nodes in AWNs. We now show that the problem
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of finding OVMT is NP-complete.
Theorem 1. Given a graph G = (V,E), source node s
∈ V , and receiver set R ⊆ V, the problem of finding OV MT
is NP-complete.
Proof: Assume that the OV MT problem can be solved in
polynomial time with an algorithm called OVMT Algo. Since
OV MT Algo can be applied for any number of receivers
1 ≤| R |≤ n where n =| V |. Let the receiver set, R contain
all nodes of G, i.e. | R |= n. Using OV MT Algo, and for all
ϑ ∈ V as root node and R=V -{ϑ}, construct OV MT. Let the
OV MT for each case be T1,T2,T3,···,Ti; where 1 ≤ i ≤ n.
Each tree Ticontains | V | nodes, Eiedges, and Rireceivers
where Ri=V -{ϑi} with ϑi as its root node. Of all the trees
T1,T2,T3,···,Tn, find the trees where s is a non-leaf node.
Let these trees be M1,M2,M3,···,Mk; where 1 ≤ k ≤ n.
Now from all the trees M1,M2,M3,···,Mk find the tree
(break the ties randomly) whose number of non-leaf nodes is
minimum. Call that tree as Mj. Mjfits the definition of Opti-
mal Broadcast Tree (OBT) as Mjcontains minimum number
of non-leaf nodes, i.e., we solved the OBT problem in polyno-
mial time which is a contradiction to the OBT problem, which
has been proved to be NP-complete by Lim and Kin in [13].
Since a special case of OV MT problem (| R |= n) is NP-
complete, the OV MT problem must be at least as hard as NP-
complete.
Figure 2.Different possible cases in LDMT heuristic.
Algorithm 1 Localized Distributed heuristic for Minimum
number of Transmissions (LDMT)
R ← all receiver node ids which are not within the trans-
mission range (single-hop) of Source node S
lmi← minimum hop length from source seen by node i
plmi← previous node along lmipath seen by node i
Nrssi← number of receivers seen along lmipath by node i
N(ri) ← the set of neighbor nodes of receiver ri
Nr(ni) ← the set of neighbor receivers of a node ni, i.e.,
all the receivers that are within the single hop distance to
node ni
NC(ni) ← the set of neighbor receivers that are con-
nected to ni, i.e., all the receivers that are within the single
hop distance to node niand connected to node nito receive
multicast voice packets.
Begin
(1) Source node S broadcasts SrcJoinAdvt packet:
SrcJoinAdvt(lmi= 0, plmi= S.id, Nrssi= 0);
(2) At node ni
if Received non Duplicate SrcJoinAdvt packet with better
hop length, lmithen
Update the variables: lmi, plmi, and Nrssi
if ni∈ R then Nrssi= Nrssi+ 1 end if
end if
Forward the SrcJoinAdvt packet: SrcJoinAdvt(lmi=
lmi+ 1, plmi= i, Nrssi);
(3) Each receiver, ri ∈ R, issues a 1-hop broadcast
message
C Req
with
< ri.id,lmi,plmi,Nrssi>.
(4) Now each nj ∈ N(ri) replies with C Reply message
with the following 6-tuple:
< Nrssj,lmj,plmj,Nr(nj),NC(nj),nj.id >.
(5) Identify the CONNECTING NODE of receiver ri∈ R
(a) if ri ∈ R gets a reply from only one neighbor then
connect to it. /* this case is shown in Fig. 2(a) */
(b) if ri∈ R gets a reply from a neighbor which is also a
receiver (say rj) and if lmi= lmjthen
if |NC(ni)| < |NC(nj)| then
Connect rito rj /* Since rj has high connectivity than
ri. See Fig. 2(c) */
else
if |NC(ni)| = |NC(nj)| then
/*Connectivities of both nodes niand njare equal:
See Fig. 2(b)*/
if Nrss(ni) > Nrss(nj) then
Connect rjto ri/* since rihas higher Nrss value
than rj*/
else
Connect rj to ri /* giving more priority to min.
node-id */
end if
end if
end if
end if
(c) if a receiver rihas a neighbor fj (where fj is a node
in the multicast tree which is neither source node nor a
multicast receiver node) and if N(fj) contains a receiver rk
and fjis at d+1 distance from the Source with plmj= ri,
then rk must be at least d + 1 distance away from the
Source. This information is useful to take a decision on to
which rior rkis to be connected. /* this case is shown in
Fig. 2(d) */
(6) The receivers which are able to connect to their CON-
NECTING NODES will send a JOIN message confirming
their willingness to join with the CONNECTING NODES.
(7) Now all CONNECTING NODES act as receiver nodes
and issue a 1-hop broadcast message to their neighbors and
steps (3) - (6) will be repeated. Nodes that already issued
a JOIN message will not respond now.
(8) Step (7) is stopped when all CONNECTING NODES
are exhausted.
End
thefollowing4-tuple:
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Figure 3.
indicates that the connection is established between them. A dotted line between two nodes indicates that the connection is not yet established between them.
A double circled node represents that it is acting as a forwarding node.
An example that illustrates the LDMT heuristic. S is the source and B, D, E, and F are multicast receivers. A solid line between two nodes
D. Approximation Algorithm
We observe that there exists a closely related problem in
graph theory for finding the OVMT, known as Connected
Minimum Vertex Cover (CMVC) problem. A simple algorithm
for solving the unweighted CMVC problem that gives a factor
2 approximation exists in the literature. That is, we can find
a voice multicast tree whose optimality (in terms of NFNs) is
at the maximum twice that of OVMT. The idea is as follows.
A Depth First Search (DFS) is done on the graph, and all the
non-leaf vertices are taken as the nodes in the vertex cover.
This clearly induces a connected graph, and the approximation
ratio is 2, as shown by Savage [14]. In practice, however
this method gives large connected vertex covers and also it
is a centralized algorithm making it unsuitable for AWNs. In
the next section, we propose an efficient localized distributed
heuristic algorithm for AWNs.
III. LOCALIZED DISTRIBUTED HEURISTIC ALGORITHM TO
APPROXIMATE OPTIMAL VOICE MULTICASTING TREE
The basic idea of Localized Distributed heuristic for
Minimum number of Transmissions (LDMT) is to reduce
the number of non-leaf nodes in the tree so that it will
minimize the total number of transmissions required for voice
multicasting. Each receiver tries to connect to a forwarding
node that is already feeding at least one another receiver node.
The detailed step by step mechanism is given in Algorithm 1.
We illustrate the working mechanism of LDMT heuristic
with an example. Assume that Fig. 1(a) represents an AWN.
Let S be the source node and receiver set R = {B,D,E,F}.
Initially source S broadcasts a SrcJoinAdvt message
announcing the availability of voice multicasting (step-1 in
the Algorithm 1) service. This SrcJoinAdvt packet contains
three fields (i) Minimum hop length path, lmi, from the
source, (ii) Previous node corresponding to the minimum hop
path, plmi, and (iii) Number of receiver nodes seen (Nrssi)
along the minimum hop path. On receiving a non-duplicate
SrcJoinAdvt message which has better lmi, each node saves
the current values of lmi, plmi, and Nrssiand updates them
before forwarding the SrcJoinAdvt packet (step-2 in the
Algorithm 1). After some STABILIZATION TIME,
assuming that SrcJoinAdvt is received by all receivers in the
network, each receiver ri issues a 1-hop broadcast message
C Req to get the details of its neighbor nodes, in order to
find its upstream CONNECTING NODE (step-3 in the
Algorithm 1). After a SHORT SPAN, each neighbor of
ri, nj ∈ N(ri), sends C Reply packet with < Nrssj, lmj,
plmj, Nr(nj), NC(nj), nj.id > (step-4 in the Algorithm 1).
We define CONNECTIV ITY , NC(ni) of a node, ni, as
the set of receiver nodes lying in its transmission range and
already connected to node ni. After receiving the replies each
receiver riuniquely identifies its CONNECTING NODE
and issues a JOIN message to its connecting node. There
are 4 different cases depending on the type of nodes present
in the neighborhood of a receiver node ri. These sub-cases
are shown in Figs. 2(a)-2(d) and are explained in steps
5(a)-5(c) of Algorithm 1. An important point to be considered
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TABLE I
SIMULATION PARAMETERS
Parameter
Terrain Area
Channel Capacity
Mobility Model
Source data rate
MAC Protocol
Traffic Type
Value
1,200 m x 800 m
11 Mbps
Random Way Point
50 pkts/s
802.11 DCF
CBR
Parameter
Tx. Range
# of Nodes
Sim. Duration
# of Receivers
Voice Frame Size
ipt
Value
250 m
75
900 s
25
253 bits
20 ms
is
priority
NodeId] in the same order. That is, while choosing a
CONNECTING NODE, a receiver rj gives highest
priority to NC(nj), then to lmj, and so on. Once all receivers
get connected totheir
all the
CONNECTING NODES
receiversandthewholeprocess
CONNECTING NODES are exhausted. Fig. 3 shows
a step-by-step mechanism of computing the OVMT using
LDMT heuristic. Fig. 3(a) shows when all receivers send a
1-hop broadcast message C Req. Note that since receiver B is
within the transmission range of source S, it will not broadcast
any C Req packet. Each neighbor, ni, of these receiver nodes
replies with < Nrssi, lmi, plmi, Nr(ni), NC(ni), ni.id >
after a small time interval SHORT SPAN. As shown in
Fig. 3(b), receivers E and F find that they have to connect
to node C. This is because the plmiof receivers E and F is
node C and thus node C is the best choice for receivers E
and F. Now receivers E and F send a JOIN packet to node
C. After receiving the C Reply from node C, the receiver D
finds that it has to connect to node C (since node C is already
feeding receivers E and F) and thus it sends a JOIN packet
to node C (see Fig. 3(c)). Now node C becomes a receiver
temporarily and follows the similar procedure to find its best
connecting node. The process is shown in Figs. 3(d)-(g). The
final multicast tree is shown in Figure 3(h).
thatwhile
must
choosing
be
a
CONNECTING NODE,
[NC(nj),givento
lmj,
Nrssj,
CONNECTING NODES,
now
isrepeated
act
till
as
all
IV. SIMULATION STUDIES
A. Simulation Framework
We use the NS-2 simulation framework [15] to evaluate
the performance of LDMT. We compare its performance with
ADMR [4] and RDVMR [5]. We compare our protocol with
ADMR and RDVMR (for the single tree case) for various
scenarios. For all experiments we set the parameters α, β, γ,
and λ for RDVMR to 0.03, 0.8, 0.2, and 2, respectively as
given in [5]. We evaluate the performance using the following
metrics: 1) Frame Delivery Ratio (FDR) (the ratio of the
average number of voice frames received by each receiver
over the number of frames sent by the source), 2) Number
of Transmissions Needed For Multicast (the total number
of transmissions taken by protocol for sending a voice frame
to all receivers in the multicast tree), 3) Normalized Packet
Overhead (NPO) (the ratio of the total number of packets
(control and data) exchanged over the total number of data
packets received by all the receivers), and 4) Measurement
of Perceptual Evaluation Speech Quality - Mean Opin-
ion Score (PESQ-MOS). The PESQ-MOS is evaluated as
follows. At each receiver, the voice frames are decoded
and the wide band version of ITU perceptual measurement
algorithm, PESQ-MOS reference software tool [17] is used
to measure their perceived voice quality. The PESQ-MOS
reference software tool compares the degraded speech with
the reference speech and computes the objective MOS value
in a 5-point score ranging from -0.5 (worst) to 4.5 (best). With
respect to a original raw voice frame, the voice quality scores
of different voice frames are evaluated using PESQ-MOS
reference software tool. The evaluated voice quality scores of
(a) raw voice frame, (b) decoded AMR-WB voice frame, and
(c) decoded bits of AMR-WB voice frame that corresponds to
basic quality are 4.5 (Ideal Quality), 3.818 (Optimal), and 2.86,
respectively. The optimal quality score (3.818) corresponds
to the decoding of AMR-WB (lossy encoded) voice frame
assuming no losses in the network.
We modified ADMR protocol to incorporate LDMT heuris-
tic in the NS-2 version 2.1b8. The simulation parameters
are shown in Table I. The source sends data throughout the
simulation period and 25 of the total nodes are randomly
chosen to be receivers. Each of these receivers joins at a
random time instant, chosen uniformly from (4,450) seconds.
The receivers do not leave the multicast session. All the results
presented in this paper were averaged over 30 simulation runs
and all the results conform to 95% confidence levels. Each
node moves with some constant speed (i.e., min speed is equal
to max speed) with zero pause time. The playback deadline is
200 ms, if a packet is not received within its playback deadline
it is considered lost. We use AMR-WB (Adaptive Multi-Rate
Wide Band) [16] speech codec with 12.65 Kbps bit rate with
a sample size of 253 bits for sending the voice packets from
the source to all the receivers in the multicast session.
B. Simulation Results
1) Number of Transmissions vs. Receivers: We fix the
periodicity of flooding SrcJoinAdvt to be 30 seconds in
all protocols for uniformity sake with a static scenario (mo-
bility = 0 m/s). As observed in Fig. 4, LDMT performs
better than ADMR and RDVMR. This is because both ADMR
and RDVMR protocols concentrate on finding shortest path
between the source and receivers either by using Shortest Path
Tree (in case of ADMR) or by using a variant of SMT (in case
of RDVMR). More importantly these protocols do not consider
Wireless Multicast Advantage and thus they limit themselves
for further improvement.
2) Effect of High Packet Rate: Under static scenario, we
measure the effect of high packet rate on all the three
protocols. It can be seen from Fig. 5 that the FDR of both
ADMR and RDVMR protocols decreases rapidly as the data
rate increases beyond 30 pkts/s. Since LDMT reduces the
NFNs, it can cope up with high packet rate up to 70 pkts/s
well without significant reduction in FDR.
3) Effect of Mobility and PESQ-MOS: We set data rate
at 50 pkts/s for this experiment. As observed in Fig. 6, the
NPO of LDMT is less compared to that of ADMR and
RDVMR protocols. This is due to the fact that the number of
transmissions (and thus overall voice packet traffic) is lesser
in LDMT compared to ADMR and RDVMR protocols. Thus
it can sustain mobility induced packet losses more easily
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