Local broadcast algorithms in wireless ad hoc networks reducing the number of transmissions.bak

Local Broadcast Algorithms inWireless Ad Hoc Networks: Reducing

the Number of TransmissionsMajid Khabbazian, Member, IEEE, Ian F. Blake, Fellow, IEEE, and Vijay K. Bhargava, Fellow, IEEE

Abstract—There are two main approaches, static and dynamic, to broadcast algorithms in wireless ad hoc networks. In the static

approach, local algorithms determine the status (forwarding/nonforwarding) of each node proactively based on local topology

information and a globally known priority function. In this paper, we first show that local broadcast algorithms based on the static

approach cannot achieve a good approximation factor to the optimum solution (an NP-hard problem). However, we show that a

constant approximation factor is achievable if (relative) position information is available. In the dynamic approach, local algorithms

determine the status of each node “on-the-fly” based on local topology information and broadcast state information. Using the dynamic

approach, it was recently shown that local broadcast algorithms can achieve a constant approximation factor to the optimum solution

when (approximate) position information is available. However, using position information can simplify the problem. Also, in some

applications it may not be practical to have position information. Therefore, we wish to know whether local broadcast algorithms based

on the dynamic approach can achieve a constant approximation factor without using position information. We answer this question in

the positive—we design a local broadcast algorithm in which the status of each node is decided “on-the-fly” and prove that the

algorithm can achieve both full delivery and a constant approximation to the optimum solution.

Index Terms—Mobile ad hoc networks, distributed algorithms, broadcasting, connected dominating set, constant approximation.

Ç

1 INTRODUCTION

WIRELESS ad hoc networks have emerged to supportapplications, in which it is required/desired to have

wireless communications among a variety of deviceswithout relying on any infrastructure or central manage-ment. In ad hoc networks, wireless devices, simply callednodes, have limited transmission range. Therefore, eachnode can directly communicate with only those within itstransmission range (i.e., its neighbors) and requires othernodes to act as routers in order to communicate with out-of-range destinations.

One of the fundamental operations in wireless ad hocnetworks is broadcasting, where a node disseminates amessage to all other nodes in the network. This can beachieved through flooding, in which every node transmitsthe message after receiving it for the first time. However,flooding can impose a large number of redundant transmis-sions, which can result in significant waste of constrainedresources such as bandwidth and power. In general, notevery node is required to forward/transmit the message inorder to deliver it to all nodes in the network. A set of nodesform a Dominating Set (DS) if every node in the network is

either in the set or has a neighbor in the set. A DS is called aConnected Dominating Set (CDS) if the subgraph inducedby its nodes is connected. Clearly, the forwarding nodes,together with the source node, form a CDS. On the otherhand, any CDS can be used for broadcasting a message(only nodes in the set are required to forward). Therefore,the problems of finding the minimum number of requiredtransmissions (or forwarding nodes) and finding a Mini-mum Connected Dominating Set (MCDS) can be reduced toeach other. Unfortunately, finding a MCDS (and henceminimum number of forwarding nodes) was proven to beNP hard even when the whole network topology is known[1], [2]. A desired objective of many efficient broadcastalgorithms is to reduce the total number of transmissions topreferably within a constant factor of its optimum. For localalgorithms and in the absence of global network topologyinformation, this is commonly believed to be very difficultor impossible [3], [4].

The existing local broadcast algorithms can be classifiedbased on whether the forwarding nodes are determinedstatically (based on only local topology information) ordynamically (based on both local topology and broadcaststate information) [5]. In the static approach, the distin-guishing feature of local algorithms over other broadcastalgorithms is that using local algorithms any local topologychanges can affect only the status of those nodes in thevicinity. Therefore, local algorithms can provide scalabilityas the constructed CDS can be updated, efficiently. Theexisting local algorithms in this category typically use apriority function known by all nodes in order to determinethe status of each node [5]. In this paper we show that,using only local topology information and a globally knownpriority function, the local broadcast algorithms based on

402 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 3, MARCH 2012

. M. Khabbazian is with the Department of Applied Computer Science,University of Winnipeg, 515 Portage Avenue, Winnipeg, MB, Canada.E-mail: [email protected].

. I.F. Blake and V.K. Bhargava are with the Department of Electrical andComputer Engineering, University of British Columbia, 2332 Main Mall,Kaiser 4112, Vancouver, BC V6T 1Z4, Canada.E-mail: {ifblake, vijayb}@ece.ubc.ca.

Manuscript received 21 July 2009; revised 17 Dec. 2010; accepted 10 Jan.2011; published online 17 Mar. 2011.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TMC-2009-07-0297.Digital Object Identifier no. 10.1109/TMC.2011.67.

1536-1233/12/$31.00 � 2012 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS

http://ieeexploreprojects.blogspot.com

the static approach are not able to guarantee a goodapproximation factor to the optimum solution (i.e., MCDS).On the other hand, we show that local algorithms based onthe static approach can achieve interesting results such as aconstant approximation factor and shortest path preserva-tion if the nodes are provided with position information.

In the dynamic approach, the status of each node (hencethe CDS) is determined “on-the-fly” during the broadcastprogress. Using this approach, the constructed CDS mayvary from one broadcast instance to another even when thewhole network topology and the source node remainunchanged. Consequently, the broadcast algorithms basedon the dynamic approach typically have small maintenancecost and are expected to be robust against node failures andnetwork topology changes. Many local broadcast algo-rithms in this category use local neighbor information toreduce the total number of transmissions and to guaranteefull delivery (assuming no loss at the MAC/PHY layer).Others, such as probability-based and counter-based algo-rithms [6], [7], [8], do not rely on neighbor information.These algorithms typically cannot guarantee full deliverybut eliminate the overhead imposed by broadcasting“Hello” messages or exchanging neighbor information.

Many of the existing neighbor-information-based broad-cast algorithms in this category can be further classified asneighbor-designating and self-pruning algorithms. In neigh-bor-designating algorithms [9], [10], [11], each forwardingnode selects some of its local neighbors to forward themessage. Only the selected nodes are then required toforward the message in the next step. For example, aforwarding node umay select a subset of its 1-hop neighborssuch that any 2-hop neighbor of u is a neighbor of at leastone of the selected nodes [9]. In self-pruning algorithms [3],[12], [13], on the other hand, each node decides by itselfwhether or not to forward a message. The decision is madebased on a self-pruning condition. For example, a simpleself-pruning condition employed in [12] is whether allneighbors have been covered by previous transmissions. Inother words, a node can avoid forwarding/rebroadcasting amessage if all of its neighbors have received the message byprevious transmissions.

In [14], it was shown that neither neighbor-designatingnor self-pruning algorithms can guarantee both fulldelivery and a constant approximation if they use only 1-hop neighbor information and do not piggyback informa-tion into the broadcast packets. The authors then proposeda self-pruning algorithm based on partial 2-hop neighborinformation and proved that the algorithm achieves aconstant approximation to the optimum solution andguarantees full delivery. However, in their proposedalgorithm, each node was assumed to have its (approx-imate) position information, which is not practical in someapplications/scenarios. Also, having position informationcan provide nontrivial information in wireless ad hocnetworks and can greatly simplify the problem. As such,we wish to know whether similar results can be obtainedwithout using position information. In this paper, weanswer this remaining question in the positive—wepropose a local broadcast algorithm based on 2-hopneighbor information and prove that it guarantees a

constant approximation to the optimum solution. Theproposed algorithm is both neighbor-designating and self-pruning, i.e., the status of each node is determined by itselfand/or other nodes. In particular, using our proposedalgorithm, each broadcasting node selects at most one of itsneighbors to forward the message. If a node is not selectedto forward, it has to decide, on its own, whether or not toforward the message.

The rest of the paper is organized as follows: In Section 2,we describe our system model and assumptions. In Sections3 and 4, we analyze the power of local broadcast algorithmsbased on the static and dynamic approach, respectively. InSection 5, we use simulation to confirm the analyticalresults presented in Section 4. Finally, we conclude thepaper in Section 6. Most of the proofs are placed in theAppendix, which can be found on the Computer SocietyDigital Library at http://doi.ieeecomputersociety.org/10.1109/TMC.2011.67.

2 SYSTEM MODEL AND ASSUMPTIONS

We assume that the network consists of a set of nodes V ,jV j ¼ N . Each node is equipped with omnidirectionalantennas. Every node u 2 V has a unique id, denotedidðuÞ, and every packet is stamped by the id of its sourcenode and a nonce, a randomly generated number by thesource node. For simplicity, we assume that all nodes arelocated in two-dimensional space. However, all the resultspresented in this paper can be readily extended to three-dimensional ad hoc networks.

To model the network, we assume two different nodesu 2 V and v 2 V are connected by an edge if and only ifjuvj � R, where juvj denotes the euclidean distance betweennodes u and v and R is the transmission range of the nodes.Thus, we can represent the communication graph byGðV ;RÞ, where V is the set of nodes and R is the trans-mission range. This model is, up to scaling, identical to theunit disk graph model, which is a typical model for two-dimensional ad hoc networks. In reality, however, thetransmission range can be of arbitrary shape as the wirelesssignal propagation can be affected by many unpredictablefactors. Finally, we assume that the network is connectedand static during the broadcast and that there is no loss atthe MAC/PHY layer. These assumptions are necessary inorder to prove whether or not a broadcast algorithm canguarantee full delivery. Note that without these assump-tions even flooding cannot guarantee full delivery.

3 BROADCASTING USING THE STATIC APPROACH

Let the k-neighborhood of a node u, denoted GkðuÞ, be thesubgraph induced by u and nodes at most k hops awayfrom u. Suppose each node is given a globally fixed priorityfunction PrðidðwÞ; Gh0 ðwÞÞwhich gets a node’s id, idðwÞ, andits local topology information, Gh0 ðwÞ, as inputs and returnsa real number that determines the priority of w. Forexample, priority of a node can be determined by its id,by its degree (i.e., the number of its 1-hop neighbors) or byits neighbor connectivity ratio (i.e., ratio of pairs ofneighbors that are not directly connected to all possiblepairs of neighbors).

KHABBAZIAN ET AL.: LOCAL BROADCAST ALGORITHMS IN WIRELESS AD HOC NETWORKS: REDUCING THE NUMBER OF... 403


In local broadcast algorithms based on the staticapproach, the status (forwarding/nonforwarding) of eachnode u, StatðuÞ, is a function of idðuÞ, GhðuÞ, and PrðidðvÞ;Gh0 ðvÞÞ, where v 2 GhðuÞ and the parameters h and h0 arefixed constant numbers.1 Note that the status of each nodedoes not depend on that of other nodes. Therefore, any localtopology change can only affect the status of the nodes inthe vicinity. In designing local broadcast algorithms, we arelooking for status functions that not only guaranteeconstructing a CDS (hence full delivery) but also ensurethat the constructed CDS has small size, preferably within aconstant factor of the optimum. In the following, we showthat no such status function exists. The idea is to find agraph in which any status function fails either in construct-ing a CDS or finding a CDS whose size is smaller than�ðNÞ, where N is the total number of nodes in the network.Our approach is to construct a graph with a large number ofnodes for which both the local topology, Ghð:Þ, and therelative priority of the nodes in Ghð:Þ are the same.

Without loss of generality, we can assume R ¼ 1. As

shown in Fig. 1, let us distribute N nodes on the x-axis

between the coordinates 0 and 2ðhþ h0Þ þ 1 such that the

coordinate of the ith node is ði�1ÞðN�1Þ � ð2ðhþ h0Þ þ 1Þ, where

1 � i � N and N � 2ðhþ h0Þ þ 1. It is easy to see that

Gh0 ðuÞ and Gh0 ðvÞ are isomorphic if u; v 2 ½h0; 2hþ h0 þ 1�.Based on the definition of priority function, the relative

priority of two nodes u and v only depends on their ids if

Gh0 ðuÞ and Gh0 ðvÞ are isomorphic. Therefore, we can

distribute all nodes in the interval ½h0; 2hþ h0 þ 1� such that

their priorities increase as their coordinates (their distance

to the origin) increase. Using this distribution, all nodes in

the unit interval ½h0 þ h; h0 þ hþ 1� will have similar views

of the local topology Ghð:Þ and priority relationship

between the nodes in Ghð:Þ. Therefore, the output of the

status function is the same for all nodes in this unit interval,

i.e., either all or none of the nodes in the unit interval will be

selected. Clearly, the latter case is not possible since at least

one node in every unit interval has to be selected (otherwise

the graph induced by the selected nodes will be discon-

nected). On the other hand, selecting all nodes in the

interval ½h0 þ h; h0 þ hþ 1� will result in a large set of

selected nodes. Note that every MCDS consists of at most

two nodes in each unit interval. Therefore, for the simple

network shown in Fig. 1, we have jMCDSj � 2 �ð2ðhþ h0Þ þ 1), where jMCDSj denotes the size of a MCDS.2

If all nodes in a unit interval are selected, the size of the

obtained CDS would be at least

N � 1

2ðhþ h0Þ þ 1

� �þ 2ðhþ h0 � 1Þ:

Since h and h0 are constant, the approximation factor wouldbe at least

b N�12ðhþh0Þþ1c þ 2ðhþ h0 � 1Þ

2� ð2ðhþ h0Þ þ 1Þ 2 �ðNÞ:

Consequently, local broadcast algorithms based on thestatic approach are not able to guarantee a good approx-imation factor in the worst case. Note that this result doesnot imply that local broadcast algorithms cannot achieve agood bound on average.

3.1 Using Position Information

In the context of broadcast algorithms based on the staticapproach, we may wish to know whether using positioninformation can help us to yield a small approximationfactor. In this section, we show that a constant approxima-tion factor is achievable if position information is available.To show this, we partition the network area into square cellsas illustrated in Fig. 2 and present simple local algorithmsthat select a constant number of nodes in each cell.

The approach of network partitioning to use geographi-cal information has been used for different purposesincluding saving energy in sensor networks, and handlingmobility in broadcast algorithms for ad hoc networks. In theprimary work by Xu et al. [15], the authors propose analgorithm that partitions the network area into square cells.To save energy, at each time, the algorithm selects one nodein each cell as active and puts other nodes in the cell tosleep. The set of active nodes must form a CDS in order tomaintain network connectivity and coverage. To guaranteethis, the proposed algorithm in [15] assumes that the sidelength of each square cell is Rffiffi

5p , where R is the radio

transmission range. However, this is not sufficient toguarantee connectivity, because some square cells maynot contain any node.3 In this section, we show under what


Fig. 1. Distributing nodes on a line segment with length 2ðhþ h0Þ þ 1.

Fig. 2. Network partitioning and possible neighbors of a cell Ci for the

case � ¼ffiffi2p

2 .

1. For the sake of generality, we consider two separate parameters hand h0.

2. To be exact, jMCDSj ¼ d l�1bN�1

l c� lN�1

e , where l ¼ 2ðhþ h0Þ þ 1.3. In [15], the authors implicitly assume that there exists at least one node

in each square cell. This assumption guarantees connectivity.


conditions the set of nodes constructed by selecting onenode in each nonempty set form a CDS. We also show thatthese conditions can be relaxed at the price of selectingmore than one yet a constant number of nodes in somenonempty cells. Therefore, the result of this section can beused to extend the work in [15] to the case where some cellsmay contain no (working) sensor due to, for example, anonuniform distribution of sensors, sensor mobility, orsensor failure.

In [16], authors use a network partitioning approach indesigning broadcast protocols for dense mobile ad hocnetworks. To handle mobility, the proposed broadcastprotocols in [16] rely on the distribution of nodes asopposed to the majority of existing broadcast protocols thatrely on the frequently changing communication topology.In this section, we focus on reducing the number oftransmissions in a general static ad hoc network. Readersmay refer to [16] for a discussion on how to handle mobilitywhen network partitioning is used.

Theorem 1. Let � > 0 and m � 1 be constant numbers. Let S be

a CDS. Suppose there are at most m nodes of S in any square

of size �R� �R. Then, we have

jSj � m2

�

� �2 !

jMCDSj;

that is, the size of S is within a constant factor of jMCDSj.

For the proof, see the Appendix, which can be found inthe online supplemental material.

As shown in Fig. 2, assume that all nodes in the networkare located in a square area of size L� L. ConsideringTheorem 1, it is natural to partition the network area intosmall square cells of size �R� �R, where � is a positive realnumber, and search for algorithms that guarantee aconstant number of selected nodes in each cell. One simplealgorithm is to select exactly one node in each nonemptycell. A node can be selected using local neighbor informa-tion as follows: Suppose each node knows the id andposition of itself and its 1-hop neighbors. Also, assume that� �

ffiffi2p

2 . Therefore, the maximum distance between any twopoints in a cell is at most R, hence all the nodes in a cell are1-hop neighbors of each other. Thus, a node can verifywhether or not it has the minimum id in the cell in which itis located. Consequently, in every cell, using local neighborinformation, the node with minimum id can select itself.Note that the set of selected nodes form a dominating set asevery node in the network is either in the set or within thetransmission range of the selected node in its cell.

Let � be a positive real number. Let Ssqð�Þ denote a setconstructed by dividing the network area into small squarecells of size �R� �R (as shown in Fig. 2) and selectingexactly one node in each nonempty cell. As explainedearlier, the set Ssqð�Þ is a dominating set if � �

ffiffi2p

2 .Therefore, we use the notation DSsqð�Þ instead of Ssqð�Þ,wherever � �

ffiffi2p

2 . In general, the graph induced by DSsqð�Þis not connected even for small values of �. Nevertheless, itcan be proven that the graph induced by DSsqð�Þ isconnected (hence, DSsqð�Þ is a CDS) if the network satisfies

any of the two conditions that we call high-connectivitycondition and high-transmission condition.

We say a network satisfies the high-connectivity conditionif there exists a constant c, 0 < c < 1, such that the networkremains connected if the transmission ranges of all nodes isreduced from R to cR. Dense networks typically satisfy thehigh-connectivity condition. For example, when the densityof nodes is high, it is expected that the network remainsconnected if all nodes reduce their transmission range to,say, 90 percent of the original. Notice that the high-connectivity condition does not require nodes to reducetheir transmission ranges. It just states that the networkremains connected if the transmission range of nodes isreduced by a constant.

The high-transmission condition is an alternative condi-tion that can guarantee the constructed DSsqð�Þ is a CDS.We say a network satisfies the high-transmission condition ifthere exists a constant c, c > 0, such that every selected nodeby the algorithm can increase its transmission range from Rto at least ð1þ cÞR by increasing its transmission power. Inthe following, we show that, if � is selected carefully, thenhigh-connectivity and high-transmission conditions canguarantee that the constructed DSsqð�Þ (by, for example,the simple local algorithm explained above) is a CDS. Thefollowing lemma is useful in proving these results.

Lemma 1. Let � be a positive real number. Let u 2 Ci and v 2 Cjbe two nodes located in two different square cells Ci and Cj,where the size of each cell is �R� �R. For any pair of nodesu0 2 Ci and v0 2 Cj we have

ju0v0j � juvj þ 2ffiffiffi2p

�R:

For the set of nodes V and any positive real number r, letGðV ; rÞ denote the graph constructed by connecting twonodes in V if and only if their euclidean distance is at most r.Using this notation, the high-connectivity condition impliesthat GðV ; cRÞ is connected for some constant c, 0 < c < 1.The following theorem shows that, for some range of valuesof �, DSsqð�Þ is a CDS if the network satisfies the high-connectivity condition.

Theorem 2. Let �, 0 < � � 1�c2ffiffi2p , be a real number. Note that

� �ffiffi2p

2 . Let DSsqð�Þ be a constructed DS by selecting onenode in each nonempty set. If GðV ; cRÞ is connected, thenDSsqð�Þ is a CDS whose size is at most d2�e

2jMCDSj.

For the proof, see the Appendix, which can be foundin the online supplemental material.

The next theorem proves that, for some range of �, theconstructed DSsqð�Þ is a CDS whose size is within aconstant factor of jMCDSj if the selected nodes increasetheir transmission range by a constant.

Theorem 3. Let �, 0 < � � minð2;cÞ2ffiffi2p , and c > 0 be real numbers.

Note that ��ffiffi2p

2 . LetDSsqð�Þ be a constructed DS by selecting

one node in each nonempty set. If every node in DSsqð�Þincreases its transmission range to at least ð1þ cÞR, then

DSsqð�Þ will be CDS whose size is at most d2�e2jMCDSj.


There are optimization techniques to further reduce thesize of a constructed DSsqð�Þ or to relax the requirement of



transmitting at higher power for many selected nodes. Forexample, suppose that node us is the selected node incell Ci. The node us is not required to increase itstransmission power if every node v within transmissionrange of any node u 2 Ci is within the transmission range ofeither us or a selected neighbor of us. This condition can beformally expressed as

8u; v s:t: u 2 Ci ^ juvj � R :

9ws 2 DSsqð�Þ s:t: juswsj � R ^ jwsvj � R:ð1Þ

Both the high-connectivity and high-transmission condi-tions can be relaxed if we allow selecting more than one yeta constant number of nodes in each nonempty cell. In thefollowing, we describe a simple algorithm that achieves aconstant approximation factor in any network GðV ;RÞwithout relying on any condition.

Suppose we divide the network into square cells withsize

ffiffi2p

2 R�ffiffi2p

2 R. All nodes in a cell are 1-hop neighbors ofeach other as the maximum distance between any two pointin the cell is R. Two different cells Ci and Cj are calledneighbors if and only if

9u 2 Ci; v 2 Cj s:t: juvj � R:

In this case, nodes u and v are called connectors of theneighbor cells Ci and Cj, and u is referred to as a connectorto the cell Cj through the node v. As shown in Fig. 2, eachcell is a neighbor of at most 20 other cells if the side of eachsquare cell is set to

ffiffi2p

2 R. Assume that each node has a list ofits 2-hop neighbors together with their positions. Suppose uis a node located in the cell Ci. The node u selects itself as amember of CDS if, based on a criteria, it is the selectedconnector to a neighboring cell Cj through a node v 2 Cj.The designed criteria must be symmetric in the sense that uselects itself as a connector to the cell Cj through the nodev 2 Cj if and only if v selects itself as a connector to the cellCi through the node u 2 Cj. As an example of a symmetriccriteria, a node u 2 Ci can select itself if and only if it has aneighbor v in a neighboring cell Cj such that juvj isminimum among all the possible connectors of the cells Ciand Cj. Any tie can be broken using, for example, nodes’ids. Note that node u has a list of its 2-hop neighbors (aswell as their positions) and therefore it can compute the setof all possible connectors between its own cell and anyneighboring cell. By Theorem 1, the constructed set is a CDSwhose size is at most 20� d2�e

2 ¼ 180 times of its optimum.Note that, to construct a smaller CDS, many of the selectednodes can be pruned using similar conditions as (1).

An important application of constructing a CDS is toemploy it as a backbone for routing. When a CDS isconstructed, only the nodes in the set are required toforward packets toward the destination. Therefore, eachpath between the source node s and destination node d canbe represented as

s; w1; w2; . . . ; wk; d;

where wi are in the CDS. Let lðs; dÞ and lCDSðs; dÞ denote the

length of shortest paths between s and d in the original graph

and the graph induced by CDS [ fs; dg, respectively. In

general, the ratio lCDSðs;dÞlðs;dÞ can be very large, in the worst case.

For example, consider a network with N > 3 nodes located

on a circle with radius R2 sinð�NÞ

such that the distance between

any two neighbors is R. In the corresponding cycle graph,

every MCDS is a simple path of length N � 3. Let s and d be

the nodes at the two ends of the path. Nodes s and d are only

3 hops away from each other. However, lMCDSðs; dÞ, the

length of the shortest path between s and d in the graph

induced by the nodes in MCDS, is N � 3. Thus

lMCDSðs; dÞlðs; dÞ ¼ N

3� 1:

Consequently, even a MCDS cannot provide a goodapproximation of a shortest path in the original graph.Theorem 4, on the other hand, shows that the length of ashortest path in CDSsqð�Þ constructed based on the high-transmission condition is at most one more than that of theoriginal shortest path.

Theorem 4. For the CDS constructed based on the high-transmission condition we have

lCDSðs; dÞ � lðs; dÞ þ 1:

Employing a symmetric criteria to construct the CDS or using(1) will change the shortest path approximation to

lCDSðs; dÞ � 2� lðs; dÞ þ 1:


4 BROADCASTING USING THE DYNAMIC APPROACH

Using the dynamic approach, the status (forwarding/nonforwarding) of each node is determined “on-the-fly”as the broadcasting message propagates in the network. Inparticular, in neighbor-designating broadcast algorithms,each forwarding node selects a subset of its neighbors toforward the packet and in self-pruning algorithms eachnode determines its own status based on a self-pruningcondition after receiving the first or several copies of themessage. It was recently proved that self-pruning broadcastalgorithms (hence broadcast algorithms based on thedynamic approach) are able to guarantee both full deliveryand a constant approximation factor to the optimumsolution (MCDS) [14]. However, the proposed algorithmin [14] uses position information in order to design a strongself-pruning condition. In the previous section, we observedthat position information can simplify the problem ofreducing the total number of broadcasting nodes. Moreover,having position information may not be practical in someapplications. Therefore, it is interesting to know if both fulldelivery and a constant approximation factor can beachieved when position information is not available. In thissection, we design a hybrid (i.e., both neighbor-designatingand self-pruning) broadcast algorithm and show that thealgorithm can achieve both full delivery and constantapproximation only using connectivity information.

4.1 The Proposed Local Broadcast Algorithm

Suppose each node has a list of its 2-hop neighbors (i.e.,nodes that are at most 2 hops away). This can be achieved in



two rounds of information exchange. In the first round,each node broadcasts its id to its 1-hop neighbors (simplycalled neighbors). Thus, at the end of the first round, eachnode has a list of its neighbors. In the second round, eachnode transmits its id together with the list of its neighbors.

The proposed broadcast algorithm is a hybrid algorithm,hence every node that broadcasts the message may selectsome of its neighbors to forward the message. In ourproposed broadcast algorithm, every broadcasting nodeselects at most one of its neighbors. A node has to broadcastthe message if it is selected to forward. Other nodes that arenot selected have to decide whether or not to broadcast ontheir own. This decision is made based on a self-pruningcondition called the coverage condition.

To evaluate the coverage condition, every node umaintains a list Listcovu ðmÞ for every unique message m.Upon receiving a message m for the first time, Listcovu ðmÞ iscreated and filled with the ids of all neighbors of u and thenupdated as follows: Suppose u receives m from its neighborv and assume that v selects w 6¼ u to forward the message.Note that w may not be a neighbor of u. However, since w isa neighbor of v, it is at most 2 hops away from u. Having id’sof v and w (included in the message), node u updatesListcovu ðmÞ by removing all nodes in Listcovu ðmÞ that are aneighbor of either v or w. This update can be done because uhas a list of its 2-hop neighbors. Since w will eventuallybroadcast the message, by updating the list, u removesthose neighbors that have received the message or willreceive it, eventually. Every time u receives a copy ofmessage m it updates Listcovu ðmÞ as explained earlier. If w ¼u (i.e., u is selected by v to forward the message), node uupdates Listcovu ðmÞ by removing only neighbors of v fromthe list. Note that in this case, u must broadcast the message.However, u has to update Listcovu ðmÞ as it needs to selectone of its neighbors from the updated list (if it is not empty)to forward the message.

Definition 1 (coverage condition). We say the coveragecondition for node u is satisfied at time t if Listcovu ðmÞ ¼ ;at time t.

Algorithm 1 shows our proposed hybrid broadcastalgorithm. When a node u receives a message m, it createsa list Listcovu ðmÞ if it is not created yet and updates the list asexplained earlier. Then, based on whether u was selected toforward or whether the coverage condition is satisfied, umay schedule a broadcast by placing a copy of m in itsMAC layer queue. There are at least two sources of delay inthe MAC layer. First, a message may not be at the head ofthe queue so it has to wait for other packets to betransmitted. Second, in contention based channel accessmechanisms such as CSMA/CA, to avoid collision, a packetat the head of the queue has to wait for a random amount oftime before getting transmitted. In this paper, we assumethat a packet can be removed from the MAC layer queue ifit is no longer required to be transmitted. Therefore, thebroadcast algorithm has access to two functions to manip-ulate the MAC layer queue. The first function is thescheduling/placing function, which is used to place amessage in the MAC layer queue. We assume that thescheduling function handles duplicate packets, i.e., it does

not place the packet in the queue if a copy of it is already inthe queue. The second function is called to remove a packetform the queue (it does not do anything if the packet is notin the queue). Note that to remove a packet from the queue,the algorithm needs to have access to the MAC layer queue.This requires a cross-layer design. In the absence of anycross-layer design, the broadcast algorithm can use a timerat the network layer. We refer the reader to [17] (Section 4)for a discussion on how to use a timer to avoid this cross-layer problem.

Algorithm 1. The proposed hybrid algorithm executed by u

1: Extract ids of the broadcasting node and the selected

node from the received message m

2: if u has broadcast the message m before then

3: Discard the message

4: Return

5: end if

6: if u receives m for the first time then

7: Create and fill the list Listcovu ðmÞ8: end if

9: Update the list Listcovu ðmÞ10: Remove the information added to the message by the

previous broadcasting node

11: if Listcovu ðmÞ 6¼ ; then

12: Select an id from Listcovu ðmÞ and add it to the

message13: Schedule the message {(*only update the selected id

if m is already in the queue*)}

14: else {(�Listcovu ðmÞ ¼ ; in this case*)}

15: if u was selected then

16: Schedule the message {(*only remove the id of the

selected neighbor if m is already in the queue*)}

17: else

18: Remove the message form the queue if u has notbeen selected by any node before

19: end if

20: end if

The proposed algorithm obeys the following:

1. u discards a received message m if it has broadcastm before.

2. If u is selected to forward the message, it schedules abroadcast (regardless of the coverage condition) andnever removes the messages from the queue infuture. However, u may change or remove theselected node’s id from the scheduled message everytime it receives a new copy of the message andupdates Listcovu ðmÞ.

3. Suppose u has not been selected to forward themessage by time t and the Listcovu ðmÞ becomes emptyat time t after an update. Then at time t, it removes themessage from the MAC layer queue (if the messagehas been scheduled before and is still in the queue).

4. If Listcovu ðmÞ 6¼ ; then u selects a node fromListcovu ðmÞ 6¼ ; to forward the message and adds theid of the selected node in the message. The selectioncan be done randomly or based on a criteria. Forexample, u can select the node with the minimum idor the one with maximum battery life-time.



5. If u has been selected to forward and Listcovu ðmÞ ¼ ; itdoes not select any node to forward the message. Thisis the only case where a broadcasting node does notselect any of its neighbors to forward the message.

4.2 Analysis of the Proposed Broadcast Algorithm

In this section, we prove that the proposed broadcastalgorithm guarantees full delivery as well as a constantapproximation to the optimum solution irrespective of theforwarding node selection criteria and the random delay inthe MAC layer (hence, the random sequence of thebroadcasting nodes). In order to prove these properties,we assume that nodes are static during the broadcast, thenetwork is connected and there is no loss at the MAC/PHYlayer. Note that even flooding cannot guarantee fulldelivery without these assumptions.

Theorem 5. Algorithm 1 guarantees full delivery.

Proof. Every node broadcasts a message at most once.Therefore, the broadcast process eventually terminates.By contradiction, assume that node d has not receivedthe message by the broadcast termination. Since thenetwork is connected, there is a path from the sourcenode s (the node that initiates the broadcast) to node d.Clearly, we can find two nodes u and v on this path suchthat u and v are neighbors, u has received the messageand v has not received it. The node u has not broadcastthe message since v has not received it. Therefore, u hasnot been selected to broadcast; thus, the coveragecondition must have been satisfied for u. As the result,v must have a neighbor w, which has broadcast themessage or was selected to broadcast. Note that all theselected nodes will eventually broadcast the message.This is a contradiction as, based on the assumption, vcannot have a broadcasting neighbor. tu

Lemma 2. Using Algorithm 1, the number of broadcasting nodesinside any disk DO;R2

centered at an arbitrary point O andwith a radius R

2 is at most 32.

Proof. All nodes inside DO;R2are neighbors of each other,

thus they receive each others messages. The broadcastingnodes can be divided into two types based on whether ornot the coverage condition was satisfied for them justbefore they broadcast the message. Recall that thecoverage condition may be satisfied for a broadcastingnode if the node has been selected to forward themessage. It is because a selected node has to broadcastthe message irrespective of the coverage condition.Consider two disks centered at O with radii R

2 and 3R2 ,

respectively. Suppose k is the minimum number suchthat for every set of k nodes wi 2 DO;3R2

, 1 � i � k, we have

9i; j 6¼ i: jwiwjj � R:

Following, we find an upper bound on k. By theminimality of k, there must exist k� 1 nodes wi 2 DO;3R2

,1 � i � k� 1, such that

8i; j 6¼ i: jwiwjj > R: ð2Þ

Consider k� 1 disks D1; . . . ; Dk�1 with radius R2 centered

at wi, 1 � i � k� 1, respectively. By (2), D1; . . . ; Dk�1 arenonoverlapping disks. Also, every disk Di, 1 � i � k� 1,

resides in DO;2R, that is the disk centered at O with radius

2R. It is because, the center of every DiskDi, 1 � i � k� 1,

is inside DO;3R2. Thus, by an area argument, we get

ðk� 1Þ �R

2

� �2 !

� �ð2RÞ2:

Hence, k � 17.We first prove that the number of broadcasting nodes

inside DO;R2 for which the coverage condition is notsatisfied is at most k� 1. We then prove the same upperbound for the number of broadcasting nodes inside DO;R2for which the coverage condition is satisfied. Conse-quently, the total number of broadcasting nodes insideDO;R2 is bounded by 2k� 2 � 32. By contradiction,suppose that there are more than k� 1 broadcastingnodes inside DO;R2

for which the coverage condition is notsatisfied. Let u1; . . . ; uk be the first k broadcasting nodesordered chronologically based on their broadcast time,and a1; . . . ; ak the corresponding selected neighbor. Thus,for every i, 1 � i � k, we have ai 2 Listcovui ðmÞ, whereListcovui ðmÞ is the list of node ui at the time it broadcaststhe message. Since u1; . . . ; uk are all in DO;R2

and for everyi, 1 � i � k, juiaij � R, we get

8i; 1 � i � k: ai 2 DO;3R2:

Thus, by the definition of k, there are two nodes ai, aj, i < j

such that jaiajj � R. The node ui is broadcast before uj and

is a neighbor of it. Therefore, uj is aware of ui’s selected

neighbor ai and removes aj from Listcovuj ðmÞ as soon as it

receives the message from ui. This is a contradiction

because aj 2 Listcovuj ðmÞ at the time uj broadcasts.It remains to prove that the number of broadcasting

nodes inside DO;R2for which the coverage condition is

satisfied is at most k� 1. By contradiction, suppose that

there are at least k broadcasting nodes inside DO;R2for

which the coverage condition is satisfied. Let v1; . . . ; vk 2DO;R2

be the first k broadcasting nodes, ordered

chronologically based on their broadcast time. Note

that a broadcasting node must have been selected (byanother node) to forward the message if its coverage

condition is satisfied. Let b1; b2; . . . ; bk be the nodes that

selected v1; . . . ; vk to forward the message. Clearly, for

every i, 1 � i � k, we have bi 2 DO;3R2. Also, for every i,

1 � i � k and every j, 1 � j � k and j 6¼ i, we get bi 6¼ bj,because each node can select at most one other node to

forward. By the definition of k, there must exist two

nodes bi and bj, i < j such that jbibjj � R. This is acontradiction because bi and bj are neighbors and bjreceives the bi broadcast message, thus vj 62 Listcovbj ðmÞas vi and vj are neighbors. tu

Corollary 1. Let u be any node in the network. Using

Algorithm 1, the number of broadcasting nodes within the

transmission range of u is at most 224.

Proof. All the nodes within the transmission range of u

(including u) are inside a disk with radius R. A disk with

radius R can be covered with at most seven disks with

radius R2 [18]. Thus, by Lemma 2, the number of



broadcasting nodes within the transmission range of u isat most 7� 32 ¼ 224. tu

Theorem 6. Algorithm 1 has a constant approximation factor tothe optimal solution (MCDS). Moreover, the approximationfactor is at most 224.

Proof. Let SMCDS be a MCDS and SAlg be the set ofbroadcasting nodes using Algorithm 1. Let u be any nodein SMCDS . By Corollary 1, the number of broadcastingnodes within the transmission range of u is at most 224.Note that every broadcasting node is within thetransmission range of at least one node in SMCDS ,because SMCDS is a dominating set. Therefore

jSAlgj � 224� jSMCDSj:ut

4.3 The Strong Coverage Condition

As proven, the proposed broadcast algorithm guarantees

that the total number of transmissions is always within a

constant factor of the minimum number of required ones.However, the number of transmissions may be further

reduced by slightly modifying the broadcast algorithm. As

explained earlier, in the proposed algorithm, a selected

node has to broadcast the message even if its coveragecondition is satisfied. Nevertheless, in some cases, a selected

node can avoid broadcasting. For example, a selected node

u can abort transmission (by removing the message fromthe queue) at time t if by time t and based on its collected

information, all its neighbors have received the message.

This idea can be generalized as follows:Suppose, for each unique message m, every node u

maintains and updates an extra list Liststru ðmÞ. Similar to

Listcovu ðmÞ, Liststru ðmÞ is created and filled with the ids of u’sneighbors upon the first reception of message m. Also,

every time u receives m, it updates Liststru ðmÞ as follows: Let

v be the broadcasting node and w 6¼ u the selected node by

v. Node u first removes the nodes in Liststru ðmÞ that areneighbors of v. If the priority of w (e.g., its id) is higher than

u, it also removes the nodes in Liststru ðmÞ that are neighbors

of w. To further reduce the number of redundant transmis-sions, a selected node can abort broadcasting m under the

following strong coverage condition.

Definition 2 (strong coverage condition). We say the strongcoverage condition is satisfied for node u at time t ifListstru ðmÞ ¼ ; at time t.

Note that the strong coverage condition is only used byselected nodes to check whether they need to broadcast.Other nodes make a decision based on the previously-defined coverage condition (a weaker condition). Thefollowing theorem states that the full delivery is guaranteedif the selected nodes abort transmissions when the strongcoverage condition is satisfied. Using a similar approach tothat used in the proof of Lemma 2, it can be proven that thisextension of the algorithm also achieves a constantapproximation factor.

Theorem 7. Suppose Alg-str is a modified version of Algorithm 1in which each node maintains two lists Listcovu ðmÞ and

Liststru ðmÞ and selected nodes can avoid broadcasting underthe strong coverage condition. Alg-str guarantees full delivery.

For the proof, see the Appendix, which can be found inthe online supplemental material.

4.4 Extending the Network Model

The results presented in the paper can be extended to thecase where the nodes are distributed in three-dimensionalspace. In other words, when the nodes are distributed inthree-dimensions it can be shown that local broadcastalgorithms based on the static approach can provide aconstant approximation if nodes have their positioninformation. By replacing circles with balls, it can besimilarly shown that Algorithm 1 can provide both fulldelivery and a constant approximation to the optimumsolution.

Algorithm 1 (the proposed algorithm based on thedynamic approach) can be extended to the case where thenodes have different transmission ranges. In this case, itcan be proved that the algorithm guarantees a constantapproximation factor if the ratio RMax

RMinis constant, where

RMax is the maximum transmission range and RMin is theminimum transmission range of the nodes in the networkand two nodes have a link iff both are in transmissionrange of each other. Similar to the proof of Theorem 6, thiscan be proved by showing that the number of broadcastingnodes inside any disk D

O;RMin

2

is constant. Also, we can usethe quasi unit disk graph to model the network [19]. In thismodel, there is a link between two nodes if their euclideandistance is less than �R, 0 < � � 1, and there is no link ifthe euclidean distance is more than R. This model is closerto reality than the unit disk graph model. Using the quasiunit disk graphs model we can show that Algorithm 1guarantees a constant approximation factor if � is constant.Similarly, the proof is by showing that the number ofbroadcasting nodes in any disk DO;�R2

is constant.

5 EXPERIMENTAL RESULTS

One of the major contributions of this work is the design ofa local broadcast algorithm based on the dynamic approach(Algorithm 1) that can achieve both full delivery and aconstant approximation factor to the optimum solutionwithout using position information. To confirm the analy-tical results, we implemented Algorithm 1, Liu et al.’salgorithm (a neighbor-designating algorithm) [9], edgeforwarding algorithm (a self-pruning algorithm) [20] andflooding in the network simulator ns-2 and evaluated theratio of broadcasting nodes (i.e., number of broadcastingnodes/total number of nodes) and end-to-end delay foreach algorithm. Table 1 summarizes the parameters used inthe ns-2 simulator. We also implemented the Wan-Alzoubi-Frieder algorithm [21] in C++ and used it as an approxima-tion of the minimum number of broadcasting nodesrequired. Note that the Wan-Alzoubi-Frieder algorithm(referred to as ratio-6 approximation algorithm) is not alocal algorithm and is only used as a benchmark as it has anapproximation factor of at most 6 [22].

Both Liu et al.’s broadcast algorithm and the edge-forwarding algorithm use position information of nodes to



reduce the total number of transmissions. Liu et al. showedthat the number of broadcasting nodes using their algo-rithm is significantly lower that that of previous notablebroadcast algorithms [20], [23]. In Liu’s algorithm, eachbroadcasting node selects a smallest group of its 1-hopneighbors such that any potential 2-hop neighbor is withintransmission range of at least one of the selected nodes. Itthen piggybacks the list of the selected nodes in themessage before broadcasting it. Upon receiving a messagefor the first time, a node schedules a broadcast if and only ifit is selected to forward; otherwise, it never broadcasts themessage. Using the edge-forwarding algorithm, each nodedivides its transmission coverage into six equal size sectors.It then decides whether or not to broadcast based onthe sector in which the broadcasting node is located, andthe position of its 1-hop neighbors that have received themessage.

To compute the number of broadcasting nodes, weuniformly distributed the nodes in a square of size1;000� 1;000 m2. We allowed only one network-widebroadcast at each simulation run, selected the next for-warding node randomly, and used the strong coveragecondition in Algorithm 1 to further reduce the total numberof transmissions.

Figs. 3 and 4 show the average ratio of broadcastingnodes for over 500 runs for each given value of the input

(i.e., the total number of nodes or the transmission range).To get the results shown in Fig. 3, we set the transmissionrange to 250 m and varied the total number of nodes from25 to 1,000. In Fig. 4, the number of nodes was fixed to 1,000and the transmission range was varied from 50 to 300 m.The transmission range and the total number of nodes wereselected from a large interval so that the simulation coversvery sparse and very dense networks as well as thenetworks with large diameters. Both Figs. 3 and 4 showthat the ratio of broadcasting nodes using Algorithm 1 issignificantly lower than that of Liu et al.’s algorithm and theedge-forwarding algorithm and is very close to theestimated minimum number of required transmissions(computed using the Wan-Alzoubi-Frieder algorithm).

We computed another metric called the algorithm delay,which we define as the time between the first and the lasttransmission in a single network-wide broadcast. Fig. 5,shows the average delay of our proposed algorithm, Liuet al.’s algorithm, and the flooding algorithm. To get these


TABLE 1Simulation Parameters

Fig. 3. Ratio of broadcasting nodes versus total number of nodes.

Fig. 4. Ratio of broadcasting nodes versus transmission range.

Fig. 5. Average delay versus total number of nodes.


results, we fixed the transmission range to 250 m and variedthe number of nodes from 25 to 1,000. Based on thesimulation results, the average delay of our broadcastalgorithm is 86 to 54 percent of that of Liu et al.’s algorithmand 87 to 71 percent of that of the flooding algorithm.

Since Algorithm 1 requires nodes to collect their 2-hopneighbor information, it is mainly suitable for networks inwhich nodes have low mobility. The network-wide broad-cast may take from a fraction of second to a few secondsdepending on the MAC layer settings, the size of thenetwork, and the amount of contention. Therefore, if theaverage distance that nodes move during the network-wide broadcast is a small fraction of R, then we expectAlgorithm 1 to achieve similar results as in the staticnetworks. Otherwise, in networks with high-mobility rates,Algorithm 1 cannot use the benefit of selecting nodes toforward the message. It is because, a node does not know atwhat time a selected node will transmit the message if theselected node is not within its transmission range. There-fore, in high-mobility settings, a node may not knowwhether any of its neighbors is covered by the transmissionof a selected node as it does not know the list of 1-hopneighbors of the selected node at the time the selected nodetransmits the message. If nodes do not select other nodes toforward, then Algorithm 1 becomes similar to the proposedalgorithm in [12]. The proposed algorithm in [12] canprovide full delivery in static networks, but it cannotguarantee a constant approximation factor. To evaluate theimpact of low mobility on the number of transmissionsrequired by Algorithm 1, we performed a simulationexperiment. As before, we distributed the nodes in a squareof size 1;000� 1;000 m2 and allowed only one network-widebroadcast at each simulation run. We set the transmissionrange to 250 m and the number of nodes to 50. At thebeginning of each run, nodes start exchanging Hellomessages. After a period of time, a random node initiatesa broadcast. During the whole simulation run, nodes moveaccording to the random waypoint mobility model [24]. Inour previous simulations experiments, nodes do notexchange Hello messages after the broadcast initiation.

Therefore, they do not take into consideration the overhead

of the 2-hop neighbor discovery messages. However, in this

setting, nodes exchange Hello messages during the whole

simulation run in order to keep the list of neighbors up-to-

date. Fig. 6 shows the effect of mobility on the number of

transmissions. The x-axis is the maximum speed set in the

random waypoint mobility model and the y-axis is the

average ratio of broadcasting nodes for at least 500 runs. As

shown in Fig. 6, the number of transmissions slightly

decreases as mobility increases. Fig. 7, shows the average

delay of Algorithm 1 decreases as mobility increases.We also evaluated the performance of Algorithm 1 in

denser networks. Fig. 8 shows the average number of

transmissions when the total number of nodes varies from

50 to 1,000. To obtain the results shown in Fig. 8, we set the

maximum speed to 10 m=s and fixed the hello message

transmission rate to one per second. The simulation results

show that for low-mobility rates, the performance (in terms

of the number of transmissions) of both Algorithm 1 and


Fig. 6. Ratio of broadcasting nodes versus maximum speed. Fig. 7. Ratio of broadcasting nodes versus maximum speed.

Fig. 8. Ratio of broadcasting nodes versus total number of nodes; max.speed ¼ 10 m/s.


Liu et al.’s algorithm are very close to the case where thenetwork is static. Also, for both algorithms, the averagenumber of nodes that do not receive a message in theaforementioned settings is less than 2.

As mentioned in Section 4, Algorithm 1 can use a back-off timer in the network layer in the absence of a cross layerdesign. Each time a node receives a message, it sets thetimer with a random number and decides upon timerexpiration whether to retransmit. Larger back-off delaysdecrease the probability of collisions and reduce thenumber of transmissions as nodes can hear more transmis-sions, hence make better decisions on whether or not toretransmit. However, as shown in Fig. 9, algorithm’s end-to-end delay linearly increases with the maximum durationof back-off timer. To obtain the results shown in Fig. 9, weset the transmission range to 250 m and considered thenetwork static. The x-axis represents the maximum back-offdelay in seconds and the y-axis represents the delay ofAlgorithm 1 in seconds.

Finally, Figs. 10 and 11, respectively, show an instance

of using our proposed algorithm and Liu et al.’s algorithm

for the same network where the total number of nodes is

400 and the transmission range is set to 250 m (broad-

casting nodes are shown by stars). As proven in [14], in

neighbor-designating algorithms based on 1-hop neighbor

information (and in Liu et al.’s algorithm, in particular)

most of the nodes around the boundary of the network

broadcast the message. This undesirable property of Liu

et al.’s algorithm can be observed in Fig. 11. Note that

these snapshots of Algorithm 1 and Liu et al.’s algorithm

are not necessarily representative of the overall perfor-

mance of the two algorithms.

6 CONCLUSIONS

In this paper, we investigated capabilities of local broadcast

algorithms in reducing the total number of transmissions

that are required to achieve full delivery. As proven, local

broadcast algorithms based on the static approach cannot

guarantee a small sized CDS if the position information is

not available. It was shown that having relative position

information can greatly simplify the problem of reducing

the total number of selected nodes using the static

approach. In fact, we showed that a constant approximation

factor is achievable using position information. Using the

dynamic approach, it was recently shown that a constant

approximation is possible using (approximate) position

information [14]. In this paper, we showed that local

broadcast algorithms based on the dynamic approach do

not require position information to guarantee a constant

approximation factor. The results presented in the paper

can be extended to the case where nodes are distributed in

three-dimensional space. Also, the proposed algorithm

based on the dynamic approach can be extended to the

case where nodes have different transmission ranges or

when the network is modeled using the quasi unit disk

graph model.


Fig. 9. Algorithm’s delay versus maximum back-off delay.

Fig. 10. An instance of using our broadcast algorithm; Transmissionrange ¼ 250 m, #nodes ¼ 400.

Fig. 11. An instance of using Liu et al.’s broadcast algorithm;Transmission range ¼ 250 m, #nodes ¼ 400.


REFERENCES

[1] M. Garey and D. Johnson, Computers and Intractability: A Guide tothe Theory of NP-Completeness. W.H. Freeman & Co., 1990.

[2] B. Clark, C. Colbourn, and D. Johnson, “Unit Disk Graphs,”Discrete Math., vol. 86, pp. 165-177, 1990.

[3] J. Wu and F. Dai, “Broadcasting in Ad Hoc Networks Based onSelf-Pruning,” Proc. IEEE INFOCOM, pp. 2240-2250, 2003.

[4] J. Wu and W. Lou, “Forward-Node-Set-Based Broadcast inClustered Mobile Ad Hoc Networks,” Wireless Comm. and MobileComputing, vol. 3, no. 2, pp. 155-173, 2003.

[5] J. Wu and F. Dai, “A Generic Distributed Broadcast Scheme inAd Hoc Wireless Networks,” IEEE Trans. Computers, vol. 53,no. 10, pp. 1343-1354, Oct. 2004.

[6] S. Ni, Y. Tseng, Y. Chen, and J. Sheu, “The Broadcast StormProblem in a Mobile Ad Hoc Network,” Proc. ACM MobiCom,pp. 151-162, 1999.

[7] Z. Haas, J. Halpern, and L. Li, “Gossip-Based Ad Hoc Routing,”Proc. IEEE INFOCOM, pp. 1707-1716, 2002.

[8] D.Y. Sasson and A. Schiper, “Probabilistic Broadcast for Floodingin Wireless Mobile Ad Hoc Networks,” Proc. IEEE Wireless Comm.and Networking Conf., pp. 1124-1130, 2003.

[9] H. Liu, P. Wan, X. Jia, X. Liu, and F. Yao, “Efficient FloodingScheme Based on 1-Hop Information in Mobile Ad Hoc Net-works,” Proc. IEEE INFOCOM, 2006.

[10] J. Wu, W. Lou, and F. Dai, “Extended Multipoint Relays toDetermine Connected Dominating Sets in Manets,” IEEE Trans.Computers, vol. 55, no. 3, pp. 334-347, Mar. 2006.

[11] M. Khabbazian and V.K. Bhargava, “Efficient Broadcasting inMobile Ad Hoc Networks,” IEEE Trans. Mobile Computing, vol. 8,no. 2, pp. 231-245, Feb. 2009.

[12] W. Peng and X. Lu, “On the Reduction of Broadcast Redundancyin Mobile Ad Hoc Networks,” Proc. ACM MobiHoc, pp. 129-130,2000.

[13] I. Stojmenovic, M. Seddigh, and J. Zunic, “Dominating Sets andNeighbor Elimination-Based Broadcasting Algorithms in WirelessNetworks,” IEEE Trans. Parallel and Distributed Systems, vol. 13,no. 1, pp. 14-25, Jan. 2002.

[14] M. Khabbazian and V.K. Bhargava, “Localized Broadcasting withGuaranteed Delivery and Bounded Transmission Redundancy,”IEEE Trans. Computers, vol. 57, no. 8, pp. 1072-1086, Aug. 2008.

[15] Y. Xu, J. Heidemann, and D. Estrin, “Geography-Informed EnergyConservation for Ad Hoc Routing,” Proc. ACM MobiCom, 2001.

[16] Y. Chen and J.L. Welch, “Location-Based Broadcasting for DenseMobile Ad Hoc Networks,” Proc. ACM Int’l Symp. Modeling,Analysis and Simulation of Wireless and Mobile Systems, pp. 63-70,2005.

[17] A. Keshavarz-Haddad, V. Ribeiro, and R. Riedi, “DRB and DCCB:Efficient and Robust Dynamic Broadcast for Ad Hoc and SensorNetworks,” Proc. IEEE Fourth Ann. Comm. Soc. Conf. Sensor, Meshand Ad Hoc Comm. and Networks (SECON ’07), pp. 253-262, 2007.

[18] C.T. Zahn, “Black Box Maximization of Circular Coverage,” J.Research of the Nat’l Bureau of Standards B., vol. 66, pp. 181-216,1962.

[19] L. Barriere, P. Fraigniaud, and L. Narayanan, “Robust Position-Based Routing in Wireless Ad Hoc Networks with UnstableTransmission Ranges,” Proc. Fifth Int’l Workshop Discrete Algo-rithms and Methods for Mobile Computing and Comm. pp. 19-27, 2001.

[20] Y. Cai, K. Hua, and A. Phillips, “Leveraging 1-Hop NeighborhoodKnowledge for Efficient Flooding in Wireless Ad Hoc Networks,”Proc. IEEE Int’l Performance, Computing, and Comm. Conf. (IPCCC’05), pp. 347-354, 2005.

[21] P. Wan, K. Alzoubi, and O. Frieder, “Distributed Construction ofConnected Dominating Set in Wireless Ad Hoc Networks,” Proc.IEEE INFOCOM, vol. 3, pp. 1597-1604, 2002.

[22] A. Vahdatpour, F. Dabiri, M. Moazeni, and M. Sarrafzadeh,“Theoretical Bound and Practical Analysis of Connected Dom-inating Set in Ad Hoc and Sensor Networks,” Proc. 22nd Int’lSymp. Distributed Computing (DISC ’08), pp. 481-495, 2008.

[23] J. Wu and H. Li, “On Calculating Connected Dominating Set forEfficient Routing in Ad Hoc Wireless Networks,” Proc. Int’lWorkshop Discrete Algorithms and Methods for Mobile Computing andComm. (DiaLM ’99), pp. 7-14, 1999.

[24] T. Camp, J. Boleng, and V. Davies, “A Survey of Mobility Modelsfor Ad Hoc Network Research,” Wireless Comm. and MobileComputing (WCMC ’02), vol. 2, pp. 483-502, 2002.

Majid Khabbazian received the undergraduatedegree in computer engineering from the SharifUniversity of Technology, Iran, and the master’sand PhD degrees both in electrical and compu-ter engineering from the University of Victoriaand the University of British Columbia, Canada,respectively. From 2009 to 2010, he was aresearch fellow at the Computer Science andArtificial Intelligence Lab, MIT. He is an assistantprofessor in the Department of Applied Compu-

ter Science, University of Winnipeg, Canada. His research interestsinclude wireless networks, distributed algorithms, applied cryptographyand network security. He is a member of the IEEE.

Ian F. Blake received the undergraduate degreefrom Queens University, Kingston, Ontario,Canada, and the PhD degree from PrincetonUniversity, Princeton, New Jersey. From 1967 to1969, he was a research associate with the JetPropulsion Laboratory, Pasadena, California.From 1969 to 1996, he was with the Departmentof Electrical and Computer Engineering, Univer-sity of Waterloo, Ontario, Canada, where he waschairman from 1978 to 1984 and director of the

Institute of Computer Research from 1990 to 1994. From 1996 to 1999,he was with the Hewlett-Packard Labs, Palo Alto, California. He iscurrently with the Department of Electrical and Computer Engineering,University of British Columbia, Vancouver, Canada. His researchinterests are in the areas of cryptography, algebraic coding theory,digital communications, and spread-spectrum systems. He is a fellow ofthe Institute for Combinatorics and its Applications, the IEEE, and theCanadian Academy of Engineering.

Vijay K. Bhargava received the undergraduate,master’s, and PhD degrees from Queen’sUniversity, Kingston, Ontario, Canada, in 1970,1972, and 1974, respectively. Currently, he is aprofessor at the University of British Columbia,Vancouver, Canada. Previously, he was with theUniversity of Victoria (1984-2003) and withConcordia University in Montreal (1976-1984).He is a coauthor of the book Digital Commu-nications by Satellite (Wiley, 1981), coeditor of

Reed-Solomon Codes and Their Applications (IEEE, 1994), and coeditorof Communications, Information and Network Security (Kluwer, 2003).His research interests are in wireless communications. He has servedon the boards of the IEEE Information Theory Society and the IEEECommunications Society. He is a past president of the IEEE InformationTheory Society and a past editor-in-chief of the IEEE Transactions onWireless Communications. He is a fellow of the Engineering Institute ofCanada (EIC), the IEEE, the Canadian Academy of Engineering, andthe Royal Society of Canada.

. For more information on this or any other computing topic,please visit our Digital Library at www.computer.org/publications/dlib.



Local broadcast algorithms in wireless ad hoc networks reducing the number of transmissions.bak

Documents

Transcript of Local broadcast algorithms in wireless ad hoc networks reducing the number of transmissions.bak