[lecture notes in computer science] distributed computing and networking volume 4904 ||...

Energy-Efficient Dominating Tree Constructionin Wireless Ad Hoc and Sensor Networks�

Ruiyun Yu1, Xingwei Wang2, Yonghe Liu3, and Sajal K. Das3

1 Computing Center, Northeastern University, [email protected]

2 College of Information Science and Engineering, Northeastern University, [email protected]

3 Department of Computer Science and Engineering, The University of Texasat Arlington, USA

[email protected], [email protected]

Abstract. Motivated by reducing communication overhead and pro-longing network lifetime in wireless ad hoc and sensor networks, we pro-pose an energy-efficient dominating tree construction (EEDTC ) algo-rithm to construct a dominating tree that can serve as a communicationbackbone in wireless infrastructures. The algorithm has a theoreticalapproximation factor of at most 9, and has O(n) message complexityand O(n) time complexity. Due to the low message complexity, EEDTCperforms well on energy consumption. The energy-aware ranking tech-nique introduced can also balance energy consumption in the network,and hence reduce the probability of network failures caused by energydepletion of backbone nodes.

1 Introduction

Wireless ad hoc and sensor networks have drawn lots of attention in recent years.Unlike other traditional networks, they are decentralized and have no physicalbackbone infrastructure. Broadcasting feature is a nature of wireless networksand can cause high communication overhead.

To reduce communication overhead, many researchers proposed to use a con-nected dominating set (CDS ) as a virtual backbone for hierarchical routing inwireless ad hoc and sensor networks [1][2][3][4][5][6][7][8][9][10].

But constructing and maintaining a CDS will impose other control overheadonto overall communication, so a CDS -construction algorithm should be efficientenough. On one hand, the size of a CDS should be as small as possible, so thatoverhead will be minimized when an application is executed on the CDS. On theother hand, the algorithm also should have good performance on time complexityand message complexity, and try its best to reduce control overhead.� This work is supported by the National High-Tech Research and Development Plan

of China under Grant No. 2006AA01Z214, the National Natural Science Foundationof China under Grant No. 60673159, and the Program for New Century ExcellentTalents in Universities.

S. Rao et al. (Eds.): ICDCN 2008, LNCS 4904, pp. 558–569, 2008.c© Springer-Verlag Berlin Heidelberg 2008

EEDTC in Wireless Ad Hoc and Sensor Networks 559

Among existing literature, the algorithms proposed in [1], [4] and [5] are tree-based schemes. A dominating tree seems more appropriate in many applicationscenarios, such as data dissemination, data fusion, routing, and so on. Whileconstructing a dominating tree always introduces high algorithm complexity.

To construct a dominating tree with lower algorithm complexity, we proposean energy-efficient dominating tree construction (EEDTC ) algorithm, that isa quite different approach from those in [1], [4] and [5]. The differences lie inexecution processes, as well as in the amount of nodes involved.

EEDTC consists of two phases: Marking Phase and Connecting Phase. TheMarking Phase constructs a maximal independent set (MIS ), and meanwhileforms a forest consisting of trees rooted at several initiators. In the ConnectingPhase, the forest is connected to a dominating tree by connecting some adjacenttrees.

Compared with other tree-based algorithms [1][4][5], EEDTC simplifies theexecution process by combining MIS construction and forest formation togetherwhich are separated in other schemes. Moreover, only a small proportion of nodesget involved to connect the forest in EEDTC, while every node is involved up ton times in other schemes. Therefore EEDTC gains better algorithm complexity.

EEDTC has an approximation factor of at most 9, O(n) message complexityand O(n) time complexity. To the best of our knowledge, EEDTC outperformsall existing tree-based CDS -construction schemes on message complexity.

Simulations show that EEDTC performs well on energy consumption, energybalance, and message complexity.

The rest of this paper is organized as follows. We survey some of related schemesin Section 2, and introduce our contribution in Section 3. Some preliminaries andassumptions are presented in Section 4. In Section 5, we propose the EEDTC al-gorithm. Then we analyze the performance of EEDTC by theoretical analysis inSection 6 and by simulations in Section 7. Section 8 concludes this paper.

2 Related Work

In this section, we briefly survey several schemes of constructing connected dom-inating sets in wireless ad-hoc and sensor networks.

Wu and Li [2] first find a connected dominating set (CDS ) of a connectedgraph G in the Marking Process. The algorithm then removes all redundantnodes from the initial CDS in the Reducing Process.

Stojmenovic et al. [3] improve the algorithm proposed in [2] by replacinglarger-id priority with highest-degree priority to remove redundant nodes in theReducing Process.

Literature [6] and [7] take energy issue into consideration. Instead of the id-based removal approach exploited in [2], Wu et al. [6] consider two extendedrules for selective removal. In [7], Kim et al. propose an algorithm similar to theone in [11], but Kim et al. consider residual energy of each node.

The algorithms in [8], [9] and [10] are based on the multipoint relays (MPR)approach proposed in [12]. Adjih et al. [8] propose a source-independent MPR

560 R. Yu et al.

that constructs a CDS based on the original MPR algorithm. Wu et al. [9]extend the source-independent MPR by providing several extensions. Liang etal. proposed a gateway multipoint relays (GMPR) scheme in [10].

The algorithms proposed in [1], [4] and [5] are tree-based.Sivakumar et al. [1] first construct a dominating set S. Then it connects S to a

connected dominating set by using the minimum spanning tree (MST ) algorithmproposed in [13].

The algorithm proposed by Wan et al. [4] consists of two phases which con-struct a maximal independent set (MIS ) and a dominating tree, respectively. Thealgorithm runs on the basis of a spanning tree constructed by the distributedleader-election algorithm in [14].

Min et al. [5] also first construct a spanning tree using the same approach asin [4] prior to the MIS formation. Then it interconnects nodes in the MIS to aspanning tree using the distributed algorithm proposed in [14].

3 Our Contribution

The EEDTC algorithm we propose is different from those in [1], [4] and [5] onexecution processes.

The algorithm in [1] first constructs a dominating set which is then connectedby the MST algorithm in [13]. The algorithms in [4] and [5] all construct a treeusing the algorithm in [14] before the CDS construction.

The tree construction approaches in [13] and [14] all have high message com-plexity, because every node is involved up to n times to collect informationfor combination decision. Either all nodes report to the root [14], or the rootbroadcasts a query and gets response over the tree [13].

EEDTC first constructs a MIS, and meanwhile a forest consisting of somemulti-hop trees is formed with a little extra overhead. Then it connects theforest using the shortest paths between some pairs of adjacent trees.

EEDTC combines MIS construction and forest formation together, and onlya small proportion of nodes are involved to connect the forest, therefore it useless messages than in other schemes.

The algorithm in [1] has O(n|C| + m + nlogn) message complexity, and thealgorithms in [4] and [5] both have O(nlogn) message complexity, while themessage complexity of EEDTC is O(n).

Lower message complexity definitely leads to lower energy consumption. More-over, EEDTC also has good performance on energy balance. So EEDTC isenergy-efficient, and can greatly prolong the lifetime of wireless networks.

4 Preliminaries and Assumptions

We assume that the transmission ranges of all nodes in the network are equal.Without losing generality, we model the network as a unit disk graph G(V, E)[15], where V denotes the vertex (node) set and E denotes the edge set.


A subset S of V is a dominating set if each node u in V is either in S or isadjacent to a certain node v in S. A subset C of V is a connected dominatingset (CDS ) if C is a dominating set and C also induces a connected subgraph ofG. Naturally, the nodes in C can communicate with each other without usingnodes in (V − C), and every node in G can be accessed by a certain node in Cwithin one-hop distance.

A subset R of V in a graph G is an independent set if, for any pair ofvertices in R, there is no edge between them. A subset M of V is a maximalindependent set (MIS ) if no more vertices can be added into it to generate alarger independent set. From the definition, it is easy to know that a maximalindependent set (MIS ) is also a dominating set.

We assume that nodes in the network are uniquely indexed and can gauge itsresidual energy. Furthermore, through message exchanges, a node is aware of itsneighbor nodes, including their IDs and residual energy.

We also assume that nodes are static or can be viewed as static during areasonable period of time.

Since the connected dominating set (CDS ) we construct in EEDTC is also adominating tree, we will use these two phrases interchangeably in the remainderof this paper.

5 The Energy-Efficient Dominating Tree Construction(EEDTC ) Algorithm

Our algorithm towards the construction of a dominating tree is named EEDTC(the energy-efficient dominating tree construction). It consists of two phases:Marking Phase and Connecting Phase. The Marking Phase constructs a MIS(as discussed in the previous section, a maximal independent set (MIS ) is alsoa dominating set), and a forest composed of trees rooted at several initiators isgenerated at the same time, then the Connecting Phase connects the forest to asingle spanning tree, in which a subset of nodes form a dominating tree.

5.1 Marking Phase

The goal of this phase is to construct a MIS. Meanwhile, the MIS will be con-nected to a forest by some intermediate nodes.

We first introduce an energy-aware ranking technique. A node has a higherrank if it has more residual energy, and node IDs are used to break a tie whennodes have equal energy.

During the Marking Phase, each node is initially a candidate, and subse-quently becomes a dominator, a connector or a dominatee. All dominators forma MIS, connectors are intermediate nodes responsible for connecting the MIS toa forest, and other nodes are dominatees.

At the beginning, a candidate with the highest rank compared with all itsneighbors turns into a dominator, then broadcasts a DOMINATOR message. Italso becomes the root of a tree, and the tree is marked by the ID of this node.

562 R. Yu et al.

Upon receiving a DOMINATOR message, a candidate changes to a dominatee,and selects the sender as its parent. Subsequently, it broadcasts a DOMINATEEmessage.

Upon receiving a DOMINATEE message, a candidate changes to a dominatorif there are no candidates with a higher rank than itself in its vicinity. Then itselects the neighbor closest to the root (with fewest hops to the root) while withhigher rank as its parent (When selecting a parent, the node first considers itsconnector neighbors if there exist such neighbors). Then the new dominator sendsa REQUESTPARENT message to its parent, and broadcasts a DOMINATORmessage.

Upon receiving a REQUESTPARENT message, if the node is a dominatee,it changes to a connector and broadcasts a CONNECTORNOTIFY messagenotifying the change.

The Marking Phase terminates when there are no candidates left in thenetwork.

Fig. 1 depicts an example with twenty-one nodes. After the Marking Phase,a forest with four trees is constructed (see 1(b)). The MIS is comprised of fivedominators (nodes with rank 15, 17, 19, 20 and 3) and a connector (the nodewith rank 13).

3

13

2 15 6

8

11

20

18 10

17

4

16

19

5

1

9

0

12

14

7

(a) initial topology

313

215

6

8

11

20

18 10

17

4

16

19

5

1

9

0

12

14

7

(b) the forest constructed

313

215(20,17) 6

8

11

20(19,15)

18 10

17(15,19)

4

16

19(20,17)

5

1

9

0

12

14

7

(c) final dominating tree

Fig. 1. The dominating tree construction

5.2 Connecting Phase

In this phase, we will connect the forest constructed in the Marking Phase to asingle spanning tree.

The tree construction approaches in [13] (exploited in [1]) and [14] (used by [4]and [5]) all have high message complexity, because, in each combination round,all nodes in related trees are involved to collect information for next combinationdecision, and some nodes will be involved n times in an extreme instance (forexample, a chain structure).

To minimize amount of messages used in this phase, we now propose a novelapproach to connect the forest to a spanning tree. By this approach, the forest willbe connected only through communication along the shortest paths between pairsof adjacent trees, and nodes not in these paths will not be involved in the execution.

For ease of explanation, we use an edge node to denote a node in a tree thathas more than one neighbor in other trees.


The Connecting Phase runs as follows.At the beginning, each edge node sends a FEEDBACK message to the root

of the tree it belongs to along its tree branch.Upon receiving a FEEDBACK message, a non-root node just forwards the

message.After receiving FEEDBACK messages from all edge nodes in the tree, a root

node gets information of adjacent trees, and knows the shortest paths to alladjacent trees. In the paths, only edge nodes might be dominatees, and theother nodes are either dominators or connectors.

Then, all trees in the forest will gradually be merged into the tree with thelargest ID, and eventually there is only one tree left that spans the network. Thedominatees in the shortest paths that connect the forest will become connectors.

We define a merging rule here. If a tree has at least one adjacent tree, andhas the smallest ID compared with all its adjacent trees, it will be merged intothe adjacent tree with the highest ID.

If a tree satisfies the merging rule, it first sends a MERGE message to theroot of the tree it is about to be merged into, and changes its ID to the ID ofthat tree. Then it sends a MERGENOTIFY message to the roots of any otheradjacent trees notifying the ID change.

Both a MERGE message and a MERGENOTIFY message are sent along theshortest paths between pairs of adjacent trees.

Each sender or forwarder of a MERGE message select its next-hop node inthe path as its new parent. Upon receiving a MERGE message, a node changesto a connector if it is a dominatee.

When receiving a MERGE message or a MERGENOTIFY message, a rootnode starts another merging round if it satisfies the merging rule.

The Connecting Phase terminates when there are no root nodes satisfying themerging rule, and there is just one tree left that spans the network. All domina-tors form a maximal independent set(MIS ), and all connectors are responsiblefor connecting the MIS to a dominating tree.

Fig. 1(c) shows the dominating tree we finally get. The dominators (markedwith solid dots) and the connectors (marked with solid squares) form the domi-nating tree.

6 Features of EEDTC

EEDTC constructs a maximal independent set(MIS ) in the Marking Phase. Thesize relation between any MIS and any optimal connected dominating set(CDS )in a unit disk graph G is shown in Lemma 1 which has been proved in [4].

Lemma 1. The size of any maximal independent set (MIS) of a graph G is atmost 4opt + 1, where opt is the size of any optimal connected dominating set(CDS) of a graph G.

Lemma 2. Algorithm EEDTC has an approximation factor of at most 9.

564 R. Yu et al.

Proof. The Marking Phase generates a MIS M, and a forest. We assume thenumber of trees in the forest is k. Let Mi be the set of dominators in tree i, soM =

∑ki=1 Mi

In the Marking Phase, each non-root dominator selects a connector as itsparent if there is a connector neighbor. Otherwise it selects a dominatee as itsparent and the selected dominatee becomes a connector. In an extreme situation,every non-root dominator selects a distinct connector as its parent, and thenumber of connectors in tree i is |Mi|−1. So the number of connectors introducedin the Marking Phase is at most

k∑

i=1

(|Mi| − 1) =k∑

i=1

|Mi| − k = |M | − k (1)

In the Connecting Phase, since there are k trees in the forest, we will usek − 1 paths to connect them together. Each path introduces no more than twodominatees which become connectors in the Connecting Phase. So the numberof connectors added into CDS in this phase is at most 2(k − 1).

Hence the number of connectors in CDS is no more than

|M | − k + 2(k − 1) = |M | + k − 2 (2)

And the size of CDS is at most

|M | + (|M | + k − 2) � 2(4opt + 1) + k − 2 = 8opt + k (3)

For k is the number of trees in the forest F and is equal to the number ofhigher rank initiators, it couldn’t be larger than the size of any optimal connecteddominating set (CDS ), i.e. k is less than or equal to opt.

So the approximation factor of EEDTC is at most 9opt.

Lemma 3. Algorithm EEDTC has message complexity of O(n) and time com-plexity of O(n).

Proof. Before the execution of EEDTC, every node should know all its neigh-bors’ id and residual energy. This can be achieved from broadcasting a HELLOmessage by each node in the Neighbor Discovery Phase, and the execution timeis constant. The amount of massages sent is exact one per node in this phase, sothis phase is bounded by O(1) time and O(n) messages.

In the Marking Phase, every node sends either a DOMINATOR message or aDOMINATEE message. A non-root dominator also sends a REQUESTPARENTmessage, and a dominatee sends a CONNECTORNOTIFY message when itchanges its state from dominatee to connector. These also use linear executiontime. The message complexity introduced in this phase is O(n), and the timecomplexity is O(logn).

In the Connecting Phase, every edge node in a certain tree sends a FEED-BACK message to its root node along its branch, and only nodes in the shortestpaths between adjacent trees are involved while the forest are connected, there-fore the amount of messages introduced is comparable with that in the Marking


Phase. The Connecting Phase also takes linear time. So the Connecting Phasealso takes O(n) message complexity and O(n) time complexity.

Altogether, EEDTC has O(n) message complexity and O(n) time complexity.

Instead of involving all nodes to connect a forest in [1], [4] and [5], we just usea small proportion of nodes which are in the shortest paths between pairs ofadjacent trees. Hence EEDTC gains better message complexity, and consumeless energy than other schemes. Due to the energy-aware techniques, EEDTCalso performs well on energy balance. These together earn a prolonged lifetimefor wireless networks, which is verified by the simulations in Section 7.

7 Simulation

In this section, we evaluate energy consumption, CDS size, approximation fac-tor, and message complexity of EEDTC through simulations. For performancecomparison, We also simulate the tree-based algorithm proposed by Wan et al.[4] (marked with WAN ).

The simulations run in the discrete event simulator OMNeT++ (version 3.3)[16]. The Mobility Framework (version 2.0) model [17] is used to support simu-lations of wireless networks within OMNeT++.

We assume that all nodes remain stationary throughout the simulation, andwireless nodes are randomly deployed in a 600 × 600m2 playground. The com-munication range is set to 150m.

7.1 Energy Consumption and Lifetime

According to the model proposed in [18], power consumption for sending is set to1 unit per packet (we assume all packets in our simulations are of the same size),and power consumption for receiving is set to 0.5 unit per packet. We neglectpower consumption in idle phases and computation processes. The initial energyof each node is assigned a random value between 2950 and 3000 unit.

We compare EEDTC algorithm with WAN, and also evaluate the EEDTCwith no energy awareness in which an id-priority ranking is exploited and theenergy issue is neglected.

We randomly deploy 40, 60, and 80 nodes in the playground, and simulatethree schemes for 10 rounds respectively. We don’t change the topology in eachdeployment after it is generated in the first round.

First, we simulate plain dominating tree construction processes, in which weonly construct a dominating tree in each round. As shown in Fig. 2, comparedwith WAN, EEDTC is much more efficient on energy consumption. The averageamount of energy consumed in EEDTC is only about one-fourth of that in WAN.

The dominators and the connectors are always responsible for forming a vir-tual backbone of wireless networks, and consume more energy in a communi-cation process than other nodes. To evaluate this feature, we build a set ofsimulations where a simple data query application is executed 10 times after thedominating tree construction in each round.

566 R. Yu et al.

0 5 10 15 20 25 30 35 400

500

1000

1500

2000

2500

3000

Node ID

Ene

rgy

Initial energyResidual energy (EEDTC)Residual energy (EEDTC with no energy awareness)Residual energy (WAN)

(a) 40-node simulation

0 5 10 15 20 25 30 35 40 45 50 55 600

500

1000

1500

2000

2500

3000

Node ID

Ene

rgy


(b) 60-node simulation

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800

500

1000

1500

2000

2500

3000

Node ID

Ene

rgy


(c) 80-node simulation

Fig. 2. Energy Consumption of Plain Dominating Tree Construction

0 5 10 15 20 25 30 35 400

500

1000

1500

2000

2500

3000

Node ID

Ene

rgy


(a) 40-node simulation

0 5 10 15 20 25 30 35 40 45 50 55 600

500

1000

1500

2000

2500

3000

Node ID

Ene

rgy


(b) 60-node simulation

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800

500

1000

1500

2000

2500

3000

Node ID

Ene

rgy


(c) 80-node simulation

Fig. 3. Energy Consumption with Query Applications

As illustrated in Fig. 3, energy of some nodes in WAN and in the EEDTC withno energy awareness is consumed rapidly. Due to the energy-priority ranking,EEDTC performs well on energy balance in every deployment. This remarkablyprolongs lifetime of wireless networks.

7.2 The Size of CDS

To observe the size of CDS, we run simulations with 30, 40 ,50, 60, 70, 80, 90and 100 nodes respectively, and each case is measured by 20 different topologieswhich are generated randomly.

Fig. 4(a) shows the number of dominators, connectors and CDS nodes (theunion of dominators and connectors) in 8 cases. The number of dominators inEEDTC is almost the same as in WAN, but the number of connectors is lessthan that of WAN, which leads to less CDS nodes. This owes to the connectorselection technique used in EEDTC.

However, the size of CDS varies a little when wireless nodes are evenly de-ployed in a fixed size playground and communicate at a fixed communicationradius. So when the network becomes dense, the ratio of CDS nodes to simula-tion nodes drops remarkably (see Fig. 4(b)).

7.3 Approximation Factor

The simulation setup in this part is the same as in section 7.2.


30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

22

24

26

Number of simulation nodes

Num

ber

of n

odes

in C

DS

s

CDS nodes(EEDTC)Dominator nodes (EEDTC)Connector nodes (EEDTC)CDS nodes(WAN)Dominator nodes (WAN)Connector nodes (WAN)

(a) number measurement

30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4


Per

cent

age

CDS nodes(EEDTC)Dominator nodes (EEDTC)Connector nodes (EEDTC)CDS nodes(WAN)Dominator nodes (WAN)Connector nodes (WAN)

(b) ratio measurement

30 40 50 60 70 80 90 1000.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Rat

io

EEDTCWAN

(c) ratio of connectors todominators

Fig. 4. CDS size measurement

Lemma 1 indicates that the size of any maximal independent set (MIS ) is atmost 4opt+1, and we also proved in Lemma 2 that EEDTC has an approximationof at most 9. According to Fig. 4(c), the number of the connectors is about 55to 60 percent of that of the dominators in EEDTC. So the approximation factorof EEDTC approaches to about

4opt + 1 + 0.6(4opt + 1) ≈ 6.5opt (4)

The ratio of connector number to dominator number in WAN ranges from0.6 to 0.75, so the approximation factor of WAN is about

4opt + 1 + 0.75(4opt + 1) ≈ 7opt (5)

From simulation results, the approximation factor of EEDTC is slightly betterthan that of WAN.

7.4 Message Complexity

The simulation setup in this part is the same as in section 7.2.Fig. 5 illustrates the average messages sent and received in the simulations.According to the aforementioned discussions, in EEDTC, the number of mes-

sages sent in the Neighbor Discovery Phase is exact one per node, and the Mark-ing Phase introduces no more than two messages per node. Number of messagesreceived in those two phases is decided by the average degree (see Fig. 5(c),the denser the network is, the higher the average degree is). When the averagedegree goes up, the number of messages received increases accordingly.

In the Connecting Phase, each message is unicasted along the branch its senderbelongs to or the shortest path between pairs of adjacent trees. Only a smallproportion of nodes are involved in this phase. Although some nodes may sendor receive more than one message, there are not many messages transmitted inthis phase.

As depicted in Fig 5(a), number of messages sent in EEDTC is about 4.5,and number of messages sent is directly proportional to the average degree (seeFig. 5(b) and Fig. 5(c)).

568 R. Yu et al.

30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30


Num

ber

of m

essa

ges

WANTree Construction (WAN)EEDTC

(a) average messages sent

30 40 50 60 70 80 90 1000

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320


Num

ber

of m

essa

ges

WANTree Construction (WAN)EEDTC

(b) average messages received

30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30


Deg

ree

WANEEDTC

(c) average degree

Fig. 5. Messages measurement and average degree

WAN constructs a spanning tree using the distributed leader-election algo-rithm [14] which has O(nlogn) message complexity. As shown in Fig. 5, it sendsabout 15 messages per node, and receives about 70 to 240 messages when thesimulation nodes ranges from 30 to 100. The number of overall messages sentand received in WAN subsequently increases.

These verify Lemma 3 that EEDTC has O(n) message complexity, whileWAN has O(nlogn) message complexity. Compared with WAN, EEDTC hasmuch better message complexity, which leads to a better performance on energyconsumption in EEDTC (see section 7.1).

8 Conclusion

In this paper, we propose an energy-efficient dominating tree construction(EEDTC ) algorithm to construct a connected dominating set (CDS ), and thefinal CDS we get is a dominating tree. EEDTC has a good approximation factor,as well as low message complexity and time complexity. Compared with Wan’salgorithm, EEDTC performs well on message complexity and energy consump-tion, and can greatly prolong the lifetime of wireless networks.

References

1. Sivakumar, R., Das, B., Bharghavan, V.: Spine routing in ad hoc networks. ClusterComputing 1, 237–248 (1998)

2. Wu, J., Li, H.: On calculating connected dominating set for efficient routing inad hoc wireless networks. In: DIALM 1999. Proceedings of the 3rd internationalworkshop on Discrete algorithms and methods for mobile computing and commu-nications, Seattle, USA, pp. 7–14 (November 1999)

3. Stojmenovic, I., Seddigh, M., Zunic, J.: Dominating sets and neighbor elimination-based broadcasting algorithms in wireless networks. IEEE Transactions on Paralleland Distributed Systems 13, 14–25 (2002)

4. Wan, P.-J., Alzoubi, K., Frieder, O.: Distributed construction of connected dom-inating set in wireless ad hoc networks. In: INFOCOM 2002. Proceedings of theTwenty-First Annual Joint Conference of the IEEE Computer and Communica-tions Societies, New York, USA, pp. 1597–1604 (June 2002)


5. Min, M., Wang, F., Du, D.-Z., Pardalos, P.: A reliable virtual backbone scheme inmobile ad-hoc networks. In: MASS 2004. IEEE International Conference on MobileAd-hoc and Sensor Systems, Fort Lauderdale, USA, pp. 60–69 (October 2004)

6. Wu, J., Gao, M., Stojmenovic, I.: On calculating power-aware connected dominat-ing sets for efficient routing in ad hoc wireless networks. In: IPPN 2001. Interna-tional Conference on Parallel Processing, Valencia, Spain, pp. 346–354 (September2001)

7. Kim, B., Yang, J., Zhou, D., Sun, M.-T.: Energy-aware connected dominating setconstruction in mobile ad hoc networks. In: ICCCN 2005. 14th International Con-ference on Computer Communications and Networks, San Diego, USA, pp. 229–234(October 2005)

8. Adjih, C., Jacquet, P., Viennot, L.: Computing connected dominated sets withmultipoint relays. Ad Hoc and Sensor Networks 1, 27–39 (2005)

9. Wu, J., Lou, W., Dai, F.: Extended multipoint relays to determine connected dom-inating sets in manets. IEEE Transactions on Computers 55, 334–347 (2006)

10. Liang, O., Sekercioglu, Y.A., Mani, N.: Enhanced gateway multipoint relays forconstructing a small connected dominating set in wireless ad hoc networks. In:ICCS 2006. 10th IEEE International Conference on Communication systems, Sin-gapore, pp. 1–5 (October 2006)

11. Zhou, D., Sun, M.-T., Lai, T.-H.: A timer-based protocol for connected dominatingset construction in ieee 802.11 multihop mobile ad hoc networks. In: SAINT 2005.The 2005 Symposium on Applications and the Internet, Trento, Italy, pp. 2–8(January 2005)

12. Qayyum, A., Viennot, L., Laouiti, A.: Multipoint relaying for flooding broadcastmessages in mobile wireless networks. In: HICSS 2002. The 35th Annual Interna-tional Conference on System Sciences, Hawaii, pp. 3866–3875 (January 2002)

13. Awerbuch, B.: Optimal distributed algorithms for minimum weight spanning tree,counting, leader election and related problems. In: STOC 1987. Proceedings of the19th Annual ACM Symposium on Theory of Computing, New York, USA, pp.230–240 (May 1987)

14. Cidon, I., Mokryn, O.: Propagation and leader election in a multihop broadcastenvironment. In: DISC 1998. 12th International Symposium on DIStributed Com-puting, Andros, Greece, pp. 104–119 (September 1998)

15. Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Mathemat-ics 86, 165–177 (1990)

16. Omnet++ discrete event simulator (2007), http://www.omnetpp.org17. Mobility framework model for omnet++ (2007),

http://mobility-fw.sourceforge.net18. Kubisch, M., Karl, H., Wolisz, A., Zhong, L., Rabaey, J.: Distributed algorithms for

transmission power control in wireless sensor networks. In: WCNC 2003. WirelessCommunications and Networking Conference, IEEE, New Orleans, USA, pp. 558–563 (March 2003)

http://www.omnetpp.org

http://mobility-fw.sourceforge.net

[lecture notes in computer science] distributed computing and networking volume 4904 ||...

Documents