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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

1-4244-0353-7/07/$25.00 ©2007 IEEE

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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

getconnected totheir

allthe

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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