The characteristics of wireless networks present formidable challenges to the study of broadcasting problem. A crucial issue in wireless networks is the energy consumption, because of the nonlinear attenuation properties of radio signals. Another crucial issue is the trade-off between reaching more nodes in a single hop by using higher power versus reaching fewer nodes in that single hop by using lower power. Given a wireless network with a specified source node that broadcasts messages to all other nodes in the network, the minimum energy broadcast (MEB) problem is NP-hard. In this paper, we propose a hybrid approach CBEEB(clustering-based energy-efficient broadcast) for the MEB problem based on clustering. Theoretical analysis indicates the efficiency and effectiveness of CBEEB. Simulation results show that CBEEB has better performance compared with the existing heuristic approaches

Guo, Qiang

Jiang, Honglu

Wang, Guanghui

Yu, Jiguo

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INT J COMPUT COMMUN, ISSN 1841-9836Vol.7 (2012), No. 4 (November), pp. 785-790Clustering-Based Energy-Eﬃcient Broadcast Tree in WirelessNetworksJ. Yu, H. Jiang, G. Wang, Q. GuoJiguo Yu, Honglu JiangSchool of Computer Science,Qufu Normal University, Rizhao, 276826, P.R. ChinaE-mail: jiguoyu@sina.com; jianghonglu88@163.comGuanghui WangSchool of Mathematics, Shandong University,Jinan, 250100, P.R. ChinaE-mail: ghwang@sdu.edu.cnQiang GuoKey Laboratory for Computer Networks of Shandong ProvinceShandong Computer Science Center, Jinan, 250014, P.R. ChinaE-mail: guoq@keylab.netAbstract: The characteristics of wireless networks present formidable challengesto the study of broadcasting problem. A crucial issue in wireless networks is theenergy consumption, because of the nonlinear attenuation properties of radio signals.Another crucial issue is the trade-oﬀ between reaching more nodes in a single hopby using higher power versus reaching fewer nodes in that single hop by using lowerpower. Given a wireless network with a speciﬁed source node that broadcasts messagesto all other nodes in the network, the minimum energy broadcast (MEB) problem isNP-hard. In this paper, we propose a hybrid approach CBEEB(clustering-basedenergy-eﬃcient broadcast) for the MEB problem based on clustering. Theoreticalanalysis indicates the eﬃciency and eﬀectiveness of CBEEB. Simulation results showthat CBEEB has better performance compared with the existing heuristic approaches.Keywords: Wireless Network, Energy-Eﬃcient, Broadcast, Clustering1 IntroductionNodes in wireless networks are usually powered by batteries with limited capacity. There-fore, energy eﬃciency is one of the most important design issues for wireless networks. Theenergy consumption in transmission can be further reduced by using one or more intermediatenodes instead of transmitting directly.Broadcasting in wireless networks is diﬀerent from that in wired networks, since all nodesthat are within the transmission range of the sender can receive the transmission without anyadditional cost at the sender. This characteristic of wireless transmission is known as wirelessmulticast advantage (WMA) [1]. This allows us to seek power optimal range assignment for theenergy-eﬃcient broadcast problem. The minimum energy broadcast (MEB) problem is to ﬁnd abroadcast scheme with minimum energy consumption. The problem is also known as minimumpower broadcast (MPB) problem or minimum energy consumption broadcast subgraph (MECBS)problem [2]. We use energy and power alternatively throughout this paper.In this paper, we study the problem of broadcasting in wireless networks, where every nodeis equipped with omni directional antennas. We propose a hybrid algorithm based on clusteringand prove its correctness. Theoretical analysis shows the eﬀectiveness of our approach. Wecompare it with the Broadcast Incremental Power (BIP) [1] algorithm and the best heuristicapproaches known in [2–4] by simulation.Copyright c 2006-2012 by CCC Publications786 J. Yu, H. Jiang, G. Wang, Q. Guo2 Related workMost previously developed models for broadcasting and multicasting problems were link-based models, which does not properly reﬂect the properties of the all-wireless network environ-ment. To solve the MPB problem, Wieselthier et al. ﬁrst proposed the node-based approach(BIP)which is more suitable for wireless environment than the link-based algorithms [1]. It wassubsequently shown in [5] that the BIP algorithm has an approximation ratio between 13/3 and12. Das et al. gave an improvement procedure called r-shrink for MEB problem [6]. Cagalj etal. [7] proposed another improvement procedure called embedded wireless multicast advantage(EWMA). Kang et al. [8] generalized the EWMA into another heuristic called largest expandingsweep search(LESS). In [9], an ant-colony based approach for the problem was presented. Analgorithm called CM using ant colony optimization approach was also presented in [3]. Further-more, in [4] a simple simulated annealing algorithm with Metropolis chains of dynamic lengthwas presented. The algorithm is in fact a probabilistic version of the 1-shrink tree-improvementalgorithm described in [9]. Kang et al. [10] gave a perturbation based iterated local optimizationmethod that uses LESS as local search. In [11], Montemanni et al. presented a simulated anneal-ing approach based on r-shrink. They used sweep procedure to improve the solution obtainedthrough simulated annealing. Al-Shihabi et al. [12] developed a hybrid approach combiningnested partitioning with LP relaxation and r-shrink method. In [13], Wolf et al. proposed anevolutionary local search, which uses modiﬁed r-shrink as local search and random increase intransmission power of some nodes as mutation operator. Recently, Wu et al. [14] developed agenerational genetic algorithm that uses permutation encoding to represent a broadcast scheme.Hashemi et al. presented a simulated annealing algorithm using a special node selection mecha-nism in its neighborhood structure [2]. In [15], Singh et al. proposed a hybrid approach to theMEB problem combining a genetic algorithm with a local search heuristic, which is a modiﬁedversion of r-shrink improvement procedure [6].3 Preliminaries and modelWe consider static multi-hop ad hoc wireless networks with omni-directional transmitters,and each node can adjust its transmitting power based on the distance to the receiving node. Inthe most common power attenuation model, received signal power varies as d , where d is thedistance from the transmitter and  is an environment-dependent constant typically between2 and 5. Therefore, the transmitter power required to support the direct communication isproportional to d.To represent one wireless ad hoc network, let G = (V;E) be a directed graph, where Vdenotes the set of nodes and E denotes the set of edges, and a special node s 2 V that broadcastsmessages to all other nodes of v. The transmission energy required by a node in an arborescenceis determined by the longest edge among all edges of that arborescence. Leaf nodes do not relaymessages to any other node. Therefore, the transmission energy required by leaf nodes is zero.The total transmission energy required for the broadcast can be computed by adding the energywhich is required by each node in that arborescence.Deﬁnition 1. Min-Energy Broadcast Problem(MEB): Let G = (V;E) be a directed graph, ﬁnda broadcast tree T  E rooted at s, with the minimum energy cost Pu2V max(u;v)2Td(u; v),where d(u; v) is the distance between the nodes u and v.Clustering-Based Energy-Eﬃcient Broadcast Tree in Wireless Networks 7874 Hybrid approach–CBEEBWe now propose a hybrid approach CBEEB (clustering-based energy-eﬃcient broadcast)to MEB problem, which includes a clustering algorithm and the IBIP (improved BIP) algorithm.A special node s broadcasts messages to all other nodes of V , and each node except s hasone unique identiﬁer ID. For convenience, the notation and terminology used in the rest of thispaper are summarized in Table 1.Deﬁnition 2. Priority of nodes: For two nodes i; j 2 V nfsg,i:prio > j:prio,d(i) > d(j), or d(i) = d(j) & &ID(i) > ID(j)Table 1. Notation and TerminologyID(i) The unique identiﬁer of node ii:prio The priority of node id(i) The degree of node iN1i The set of one-hop neighbors of node ii:ch The clusterhead elected by node ii:type The type of node i, which is a clusterhead or a leaf nodeThe clustering algorithm is as follows:Step 1. Each node except s collects the information of all its one-hop neighbors N1i . Suchinformation can be acquired by each node exchanging message including its ID and priorityto its one-hop neighbors. Then each node sorts the priority for all nodes within its one-hopneighborhood.Step 2. A node i decides to become a clusterhead if either one of the following criteria issatisﬁed:(1)Node i has the highest priority in its one-hop neighborhood.(2) Node i is an one-hop neighbor of a node b. Furthermore, i has the highest priority inthe one-hop neighborhood of b.Step 3. All the clusterheads are added to the set D. Assign to each clusterhead v 2 D thetransmission range rv = maxv02N1i d(v; v0). Then, all the cluster members are the leaf nodes ofthe broadcast tree.The following Figure 1 gives an example of the clustering algorithm in a twenty-node network.123567481091213 14111516171819 20123567481091213 14111516171819 20123567481091213 14111516171819 20Figure 1a.   Random   network(n=20) Figure 1b. Red nodes are clusterheads elected                      by the clustering algorithmFigure 1c. Connect the cluster members to the clust erheadFigure 1. An example of clustering in a twenty-node network.We give the IBIP(Improved BIP) algorithm.The IBIP algorithm runs on the clusterhead set D. The cluster members elected by theclustering algorithm consist of the leaf nodes of the broadcast tree.Step 1. Initially, the tree consists of only the source node s. We begin by determining thenode that node s can reach with minimum expenditure of power.788 J. Yu, H. Jiang, G. Wang, Q. GuoStep 2. Determine which new clusterhead can be added to the tree at minimum additionalpower in the set of D. If node i is already in the tree, and node j is not yet in the tree, (i; j 2 D).If Pi;j < ri , then we add j to the tree, where Pi;j is the power required to support thetransmission between node i and j, and ri is the transmission range of node i which isassigned in the clustering algorithm.Otherwise let P 0i;j = Pi;j  maxfri ; P (i)g, where P 0i;j represents the incremental powerassociated with adding j to the set of nodes to which node i is already transmitting. Thepair fi; jg that causes the minimum value of P 0i;j is selected. Node i transmits at a powerlevel suﬃcient to reach node j. Thus, one new node is added to the tree.Step 3. This process continues until all nodes are included in the tree. The total powerrequired to maintain this tree is the sum of the transmitted powers at each of the transmittingnodes.The following Figure2 gives an example of the IBIP algorithm.s1234967 58s1234967 58Step1: s 9 Step2:s 6 Figure 2a.  Figure 2b.s1234967 58s1234967 58Step3: 6 7 Final tree Figure 2c.  Figure 2d.Figure 2. An example of IBIP algorithm in a nine-clusterhead network with source node s.5 Algorithm Analysis and SimulationTheorem 3. The set of clusterheads elected by the clustering algorithm cover all network nodes.Proof: Because each node either has the highest priority among its one-hop neighbors or hasa neighbor with the highest priority among one-hop neighbors of the node. By the deﬁnitionof the dominating set, a node either becomes a dominator itself or elects the neighbor with thehighest priority among one-hop neighbors of the node as a dominator. Thus the network has adominating set elected by the algorithm. Therefore, we conclude that the sets of clusterheadselected by the clustering algorithm can cover all network nodes. 2Theorem 4. The CBEEB algorithm has time complexity of O(M2), where M  Ndmin+1 is thenumber of clusterhead elected by the clustering algorithm and dmin is the smallest degree of nodesin the network.Proof: The clustering algorithm adopts a distributed clustering strategy. Thus, the time com-plexity of the entire network equals that of a single node O(1). In the algorithm IBIP, it runson the set of clusterheads. Obviously, the number of the clusterheads is smaller than Ndmin+1 .Moreover, the IBIP algorithm is based on the Prim’s algorithm. Thus the time complexity isO(( Ndmin+1)2). Therefore, the total time complexity of the CBEEB algorithm is O(1+M2), thatis O(M2). 2Theorem 5. The overhead complexity of control messages in the network of the CBEEB algo-rithm is O(N +M3), where M  Ndmin+1 is the number of clusterhead elected by the clusteringalgorithm and dmin is the smallest degree of nodes in the network.Clustering-Based Energy-Eﬃcient Broadcast Tree in Wireless Networks 789Proof: At the beginning of the clustering algorithm, each node broadcasts a message to collectits information of its one-hop neighbors. Therefore, the overhead complexity of control messagesin the network is O(N). The IBIP runs on the set of clusterheads elected by the clusteringalgorithm based on the Prim’s algorithm. Because we need to update the power P 0i;j at eachstep of the algorithm, the message complexity is O(M3) when a straightforward implementationis used [1]. Therefore, we can conclude that the overhead complexity of control messages in thenetwork of the CBEEB algorithm is O(N +M3). 2Comparing with the time complexity of the BIP algorithm is O(N2), and the message com-plexity is O(N3) [1]. Obviously, our algorithm CBEEB shows better eﬀectiveness.We now compare the performance of CBEEB algorithm with other six broadcast algorithmsBLiMST [1], BIP [1], CM [3], SA [4], ESA [2]and GA [15] by simulations. The simulations arecarried out in an ideal network generated over a 100  100m2 area without consideration forpacket lost. The number of network nodes changes from 25 to 250 with each increment of 25.Fig 3a. The original network topology with 150nodesFigure 3b.The topology after running clusteringalgorithmFigure 3c.The topology after running IBIP Figure 4.Energy cost comparison among sevenalgorithmsFigure 3 illustrates the backbone topology construction process using CBEEB. In Figure 4,we compare the energy cost of our algorithm with other six algorithms. The simulation resultsshow that our algorithm makes further improvements on the energy cost compared with theBliMST and BIP algorithm. CM, SA, ESA and GA algorithm can improve the energy costover the BIP algorithm. Moreover, we can see CBEEB performs better than the GA algorithmespecially when the number of nodes is large.790 J. Yu, H. Jiang, G. Wang, Q. Guo6 ConclusionsIn this paper, we propose a hybrid approach for the MEB problem in wireless networks.Compared with existing approaches, theoretical and experimental results show the superiority.As further work, we will develop fully distributed algorithms for MEB problem.AcknowledgmentsThis work was partially supported by the National Natural Science Foundation of Chinafor contract (11101243, 60373012), Natural Science Foundation of Shandong Province for con-tract(ZR2009GM009, ZR2009AM013), STPU of Shandong Province for contract (J10LG09) andTKP of Shandong Province for contract (2009GG10001014).Bibliography[1] J. E. Wieselthier, G. D. Nguyen, A. Ephremides, On the construction of energy eﬃcient broadcastand multicast trees in wireless networks, in: Proc. of INFOCOM 2000, 585-594, 2000.[2] S. M. Hashemi, Mohsen Rezapour, Ahmad Moradi, Two new algorithms for the Min-power Broadcastproblem in static ad hoc networks, Applied Math. and Compu., Vol.190, pp. 1657-1668, 2007.[3] A. K. Das, R. J. Marks, M. EI-Sharkawi, P. Arabshi, A. Gray, A cluster-merge algorithm for solvingthe minimum power broadcast problem in large scale wireless networks, in Proc. of the Milcomconference, 13-16, 2003.[4] A. K. Das, R. J. Marks, M. EI-Sharkawi, P. Arabshi, A. Gray, The minimum power broadcast problemin wireless networks: a simulated annealing approach, in Proc. of WCNC, 2057-2062, 2005.[5] P. J. Wan, G. Calinescu, X. Y. Li, O. Frieder, Minimum-energy broadcast routing in static ad hocwireless networks, in Proc. of INFOCOM, 1162-1171, 2001.[6] A. K. Das, R. J. Marks, M. EI-Sharkawi, P. Arabshai, A. Gray, r-shrink: a heuristic for improvingminimum power broadcast trees in wireless networks, in Proc. of GLOBECOM 523-527, 2003.[7] M. Cagalj, J. P. Hubaux, C. Enz, Minimum-energy broadcast in all-wireless networks: NP-completeness and distribution issues, in Proc. of MobiCom’02, 172-182, 2002.[8] I. Kang, R. Poovendran, Broadcast with heterogeneous node capability, in Proc. of GLOBECOM4114-4119, 2004.[9] A. K. Das, R. J. Marks, M. EI-Sharkawi, P. Arabshi, A. Gray, The minimum power broadcast problemin wireless networks: an ant colony system approach, in Proc. of the IEEE CAS Workshop on WirelessCommunications and Networking, 5-6, 2002.[10] I. Kang, R. Poovendran, Iterated local optimization for minimum energy broadcast, in: Proc. ofWiOpt, 332-341, 2005.[11] R. Montemanni, L. M. Gambardella, A. K. Das, The minimum power broadcast in wireless networks:a simulated annealing approach, in Proc. of WCNC, 2057-2062, 2005.[12] S. Al-Shihabi, P. Merz, S. Wolf, Nested portioning for the minimum energy broadcast problem,inProc. of LION 2, LNCS 5313, 1-11, 2008.[13] S. Wolf, P. Merz, Evolutionary local search for the minimum energy broadcast problem,in Proc. ofEvoCOP’08, LNCS 4972, 61-72, 2008.[14] X. Wu, X. Wang, R. Liu, Solving minimum power broadcast problem in wireless ad hoc networksusing genetic algorithm,in Proc. of CNSR, 203-207, 2008.[15] Alok Singh, Wilson Naik Bhukya, A hybrid genetic algorithm for the minimum energy broadcastproblem in wireless ad hoc networks, Applied Soft Computing, Vol.11, pp. 667-674, 2011.

Clustering-Based Energy-Efficient Broadcast Tree in Wireless Networks

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Clustering-Based Energy-Efficient Broadcast Tree in Wireless Networks

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