J Control Theory Appl 2011 9 (1) 133–139 DOI 10.1007/s11768-011-0232-y
An energy-driven unequal clustering protocol for heterogeneous wireless sensor networks Jiguo YU 1 , Yingying QI 1 , Guanghui WANG 2 1.School of Computer Science, Qufu Normal University, Rizhao Shandong 276826, China; 2.School of Mathematics, Shandong University, Jinan Shandong 250100, China
Abstract: Due to the limitation of energy resources, energy efficiency is a key issue in wireless sensor networks (WSNs). Clustering is proved to be an important way to realize hierarchical topology control, which can improve the scalability and prolong the lifetime of wireless sensor networks. In this paper, an energy-driven unequal clustering protocol (EDUC) for heterogeneous wireless sensor networks is proposed. EDUC includes an unequal clustering algorithm and an energy-driven adaptive cluster head rotation method. The unequal size of clusters can balance the energy consumption among clusters, and the energy-driven cluster head rotation method can achieve the balance of energy consumption among nodes within a cluster, which reduces the waste of energy. Simulation experiments show that EDUC balances the energy consumption well among the cluster heads and prolongs the network lifetime. Keywords: Wireless sensor network; Unequal clustering; Cluster head rotation; Energy-driven
1
Introduction
Since wireless sensor networks have limited energy resources, energy efficiency is a key issue in designing the topology, which affects the lifetime of sensor networks greatly. Clustering is an important way to realize hierarchical topology, which becomes an effective scheme in increasing the scalability and lifetime of wireless sensor networks, and an important way for topology control. In clustering networks, nodes are grouped into clusters. Each cluster has several cluster members and a leader, often referred to as the cluster head. Each cluster member collects local data from the environment periodically and then sends the data to the cluster head. When the data from all the cluster members is received, the cluster heads aggregate the data and send it to the base station (BS). As cluster heads are responsible for receiving and aggregating the data from their cluster members and transmitting the aggregated data a long distance to BS, the energy consumption of cluster heads is much larger than that of cluster members. In order to balance the energy among nodes, most clustering protocols adopt a cluster head rotation mechanism. Cluster head rotation methods used by the existing clustering algorithms can be divided into time-driven cluster head rotation and energy-driven cluster head rotation. In time-driven clustering algorithms [1∼5], the role of cluster head is rotated in the entire network periodically according to a predetermined time threshold. This method can effectively balance the network energy consumption. At the same time, since each round of cluster head rotation is carried out in the entire network, the large overhead that occurs every time clusters are reformed causes a lot of unnecessary waste. In addition, none of the existing algorithms in this class gives the optimal value of the period. In energy-driven clustering algorithms [6∼9], the roles of cluster head are ro-
tated when the residual energy of cluster head is less than a threshold. Cluster topology maintenance only happens during local cluster head rotation. Thus, the large cost of global topology reconstruction is avoided. Aside from the energy consumption imbalance mentioned above, there is another energy consumption imbalance among cluster heads that can impact the network lifetime significantly. There are two models of intercluster communication (one-hop and multihop communication). In both models, there is an unavoidable problem of imbalanced energy dissipation among different nodes, leading to the situation that some nodes die prematurely, which can reduce the lifetime of sensor networks. For one-hop communication, the nodes far away from the BS have to transmit data to a long distance and die first, while in multihop communication, the nodes close to the BS are burdened with a heavy relay traffic load and die first (i.e., the “hot spot” problem in [10] or the “energy hole” problem in [11]). To solve this problem, a few unequal clustering algorithms are proposed by researchers to balance energy consumption among cluster heads. In this paper, an energy-driven unequal clustering algorithm called EDUC is proposed, which includes a distributed unequal clustering algorithm and an energy-driven adaptive cluster head rotation method. The unequal clustering algorithm uses unequal competition ranges to construct clusters of unequal sizes. The clusters farther away from the BS have smaller sizes than those closer to the BS, thus the cluster heads farther away from the BS can preserve some energy for the long-distance transmission. Based on the unequal clustering structure, an energy-driven cluster head rotation strategy is adopted to rotate the role of cluster head and balance the energy consumption. Each node plays as cluster head once only during the whole network lifetime. Therefore, the energy consumed in cluster head rotation is
Received 13 October 2010. The work was supported by the National Natural Science Foundation of China (No. 60373012, 10871119), the Natural Science Foundation (No. ZR2009GM009, ZR2009AM013), the Promotional Foundation for Middle-aged or Young Scientists (No. BS2009DX024), and the EDRP of Shandong Province (No. J10LG09). c South China University of Technology and Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2011
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minimized. The rest of the paper is organized as follows. Section 2 covers the related works in this area. Section 3 exhibits the network model and the energy model in our algorithm. Section 4 presents the energy-driven unequal clustering algorithm in detail. Section 5 analyzes several properties of the algorithm. In Section 6, we detail our simulation efforts and the analysis of results obtained. Finally, Section 7 concludes the paper and points out the future work.
2
Related work
LEACH [1] is a typical clustering protocol proposed for periodical data gathering applications in wireless sensor networks. In LEACH, each node independently elects itself as a cluster head with a probability. Cluster heads receive and aggregate data from cluster members and then send the aggregated data to the BS by single-hop communication. In order to balance energy dissipation, the role of cluster head is periodically rotated among the nodes. LEACH protocol is simple and does not require a large communication overhead. However, the performance in heterogeneous networks is not very well, because it does not elect cluster heads based on residual energy of nodes. To solve the “hot spot” problem, the authors in [12] propose an unequal clustering algorithm. The network field is divided into cirques. Clusters in the same cirque have the same size, while clusters in the different cirques have different sizes. Deploying some high-energy nodes take on the cluster head role to control network operation and ensures that the energy dissipation of these cluster heads is balanced. The algorithm can effectively prolong network lifetime. However, some high-energy nodes are needed to play as cluster heads, and the positions of cluster heads must be calculated previously, which may not be true for the real situation. Xiang in [13] proposes a cirque-based static clustering algorithm for multihop wireless sensor networks. Similar to reference [12], the circular network field is divided into cirques. Clusters closer to the BS have smaller sizes, so that a part of the cluster heads’ energy can be preserved for forwarding. Furthermore, a continuous working mechanism is given for reducing the energy consumption of cluster reform and prolonging the network lifetime. EEUC [4] is a distributed unequal clustering algorithm that elects cluster heads based on the residual energy of nodes. Tentative cluster heads use uneven competition ranges to construct clusters of uneven sizes. The clusters closer to the BS have smaller sizes than those farther away from the BS; thus, the cluster heads closer to the BS can preserve some energy for the intercluster data forwarding. In this way, the energy consumption among cluster heads is balanced. Similar to LEACH, EEUC adopts time-driven cluster head rotation that may cause a lot of unnecessary waste inevitably. In [6], the authors propose EDAC, and give the threshold function: Threshold = P · EC , where P is a constant proportional parameter, and EC is the energy that is left when the node is selected to be cluster head. In the data collection phase, if the cluster head finds its energy left to be less than the threshold, it triggers the cluster rotation in its cluster. It is proved by simulation that the lifetime of nodes in EDAC is longer than those in LEACH in heterogeneous networks,
and that it also works as well as LEACH in homogeneous networks. Gamwarige et al. propose another energy-driven clustering algorithm EDCR in [7]. Later, they present theoretical analysis of the performance parameters of EDCR and explain how to find the optimal values for such parameters in order to maximize the network lifetime in [14]. Furthermore, in order to further prolong the network lifetime, Gamwarige et al. extend EDCR in multihop networks and propose EDCR-MH in [15]. In these energy-driven clustering algorithms mentioned above, when the residual energy of the nodes is low, cluster head rotation will become increasingly frequent. As a result, a lot of energy is wasted in frequent cluster head rotation. Furthermore, none of these algorithms consider the solution to the “hot spot” problem. Compared with existing works, the proposed EEUC has the following advantages: 1) It adopts an unequal clustering approach to solve the “hot spot” problem in WSNs. 2) It has the ability to handle energy heterogeneity problem in WSNs. 3) The cluster heads are generated by local competition. Thus, the distribution of cluster heads is well. 4) It adopts an energy-driven cluster head rotation strategy, in which each node plays as cluster head once at most during the whole network lifetime. Therefore, the energy consumed in cluster head rotation is minimized.
3 Network model 3.1 Network model To simplify the network model, we adopt few reasonable assumptions as follows: 1) There are N sensor nodes that are distributed randomly in an M × M square field. 2) All the nodes and the BS are stationary after deployment. 3) All the sensor nodes are heterogenous. 4) All the sensor nodes are location unaware. 5) All the nodes can use power control to vary the amount of transmit power. The generated cluster heads communicate with the BS directly. 6) The BS is out of the sensor field. It has a sufficient energy resource, and the location of the BS is known by each node. 7) Each node has an identity (ID). 3.2 Energy model We adopt the energy model in EEUC [4]. To transmit an l-bit message to a distance d, the radio expands energy: l × Eelec + l × fs × d2 , d < d0 , (1) ETx (l, d) = l × Eelec + l × mp × d4 , d d0 , where d is the transmission distance, l is the length of the packet. Eelec , fs , and mp are parameters of the transmission/reception circuitry, respectively. Depending on the distance between the transmitter and receiver, free space (fs ) or multipath fading (mp ) channel models is used. 2fs . d0 = mp
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Its value is approximately equal to 87. Here, to simplify the energy model, we denote the equation as (2) ETx (l, d) = l × Eelec + l × × dn . While receiving, the radio expands energy: (3) ERx (l) = l × Eelec . In addition, we assume that the energy for data sensing is Esen , and the energy for data aggregation is Ecom .
tance from the nodes in the network to the BS, di is the distance from node i to the BS, α is a weighted factor whose value is in [0, 1], and Rmax is the maximum value of competition radius. From the above formula, we can see that the competition radius of the node is determined by di . The larger di is, the smaller RCi is. The diameter of cluster dominated by node i is
4
The subphase after cluster head competition stage is cluster formation stage, whose duration is T2 . Each non-clusterhead node chooses the nearest cluster head and sends a Join Msg that contains the ID and residual energy of this node. Cluster heads record the residual energy and distance of member nodes according to the received Join Msgs. Finally, each cluster head counts the number of its cluster members, here, we denote the number of cluster members of a cluster as C. When T2 expires, each cluster head calculates the energy threshold and generates a TDMA scheduling list according to the information of cluster members recorded above. This TDMA schedule is packaged in a Schedule Msg and broadcasted to the cluster members. Each cluster member can get the TDMA scheduling list from the received Schedule Msg. Fig. 1 illuminates the process of cluster construction phase.
EDUC details
EDUC includes two phases: cluster construction phase and self organized data collection phase. Several control messages are needed. The description of these messages are shown in Table 1. Table 1 Descriptions of control messages. Message
Description
Head Msg Join Msg Schedule Msg Trigger Msg
Tuple (selfid) Tuple (selfid, headid, selfenergy) Tuple (schedule order) Tuple (trigger time, cluster diameter)
4.1 Cluster construction phase In the network deployment phase, the BS broadcasts a signal at a certain power level. Each node can compute its approximate distance to the BS based on the received signal strength. The following phase is cluster construction phase. In T1 of time after the beginning of this phase is a subphase called cluster head competition stage. In this stage, each node computes its waiting time tw based on its residual energy. For any node i, the waiting time twi is given as follows: Ecuri (4) T 1 Vr , twi = 1 − Emax where Ecuri is the residual energy of node i, and Emax is the maximum residual energy in the network. Here, Emax can be regarded as the maximum initial energy in the network, as cluster construction phase is the first phase of the whole network. Therefore, the value of Emax is predetermined. Vr is a random value in [0.9, 1] that is introduced to reduce the probability that two nodes send Head Msgs at the same time. In the cluster head competition stage, if node i receives no Head Msg when timer twi expires, it broadcasts the Head Msg within radio range RCi to advertise its will to be a cluster head. In formula (4), a random value Vr is introduced to reduce the probability that two nodes send Head Msgs at the same time. Furthermore, each node broadcasts Head Msg within radio range RCi . Thus, the probability that multiple nodes in the same competition area have the same waiting time is very low, which means that there are few collisions among Head Msgs from multiple nodes. Otherwise, if node i receives a Head Msg from node u before timer twi expires, it records the ID of u and the distance to u. Then, it will give up the competition and become a non-cluster-head node. As a non-cluster-head node, node i can keep on receiving Head Msgs. Here, we give the formula of RCi : di − dmin (5) Rmax , RCi = 1 − α dmax − dmin where dmax and dmin is the maximum and minimum dis-
Ra = 2RCi .
(6)
Fig. 1 Description of cluster construction phase.
4.2 Self organized data collection phase In the data collection phase, each cluster member collects local data from the environment periodically and then sends the data to the cluster head within its time slot according to the TDMA scheduling list to avoid the collisions among the members in the same cluster. When the data from all the member nodes has arrived, the cluster head aggregates the data and sends it to the BS. In order to avoid the collisions
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among the nodes of neighboring clusters, a simple model of direct-sequence spread spectrum (DS-SS) is introduced. Each cluster member can only communicate with its cluster head for different clusters have different codes. In the data packet from member nodes to cluster heads, the residual energy of the member nodes is included. Cluster heads maintained an energy list based on this for the use of cluster head rotation. If the cluster head finds its residual energy to be less than the threshold, it calculates the priority of each member node in its cluster and sends the Trigger Msg to the top three nodes with the maximum priorities. The Trigger Msg contains Ra and the trigger time tai of the member node is a cluster head. Here, we choose three nodes to assure the reliability of cluster head rotation. After receive the Trigger Msg, if the non-cluster-head node received none Head Msg when timer tai expires, it will broadcast the Head Msg and become the new cluster head. The following process is like the cluster construction phase; we will not repeat again. Here, we use p to denote the priority of a node. Then, the priority of node i is pi , which is calculated based on the following formula: Ecuri dtoCHi pi = β + (1 − β) 1 − , (7) Emax dtoCHmax where dtoCHi is the distance from node i to its cluster head, and dtoCHmax is the maximum distance from member nodes to their cluster heads. Actually, dtoCHmax is a used to compare the distance from a node in the network to its cluster head. Thus, we even can choose a constant instead. β is a random value in [0.5, 1]. The trigger time of the three chosen nodes is i tai = T1 , i = 1, 2, 3. (8) 10 4.3 Threshold Ideally, in clustering networks, the energy consumed in cluster head rotation is minimum when each plays as cluster head once at most during the whole network lifetime [9]. Now, we will analyze the energy consumption of a single cluster. In data collection phase, each node collects local data and sends the data to the cluster head according the TDMA scheduling list. When the data from all the member nodes has arrived, the cluster head aggregates the data and sends it to the BS. This process is called a round of data collection. In each round, the energy consumption of all the member nodes ECM is (9) ECM = C(Eelec + Esen + dntoCH )l, where C is the number of member nodes in the cluster. dtoCH follows a uniform distribution over the interval [0, Ra ]. Consequently, the expected value of dntoCH is 2Ran . n+2 Now, substitute this in equation(9), we have 2Ran ECM = C(Eelec + Esen + )l. (10) n+2 The energy consumption of the cluster head ECH is ECH = CEelec l + Esen l + (C + 1)Ecom l +(Eelec + dndoBS )l = [(C + 1)Eelec + Esen + (C + 1)Ecom +dndoBS ]l. (11)
Thus, the total energy consumption in a cluster is Etotal = ECH + ECM = [(2C + 1)Eelec + (C + 1)(Esen + Ecom ) 2CRan )]l. (12) +(dndoBS + n+2 The energy consumption above is called effective energy cost in EDAC [6]. The energy consumed in topology construction and topology maintenance is called additional energy cost. In a round of cluster head rotation process, a cluster head needs to broadcast one Head Msg, one Schedule Msg, and three Trigger Msgs and receive Join Msgs from its cluster members. The additional energy cost of cluster head is EaCH = 5(Eelec + Ran )l + CEelec l = [(C + 5)Eelec + 5Ran ]l. (13) Each member node sends one Join Msg and receives the control messages from the cluster head. There are C member nodes in a cluster. Therefore, the total additional energy cost of all the member nodes EaCM is 2Ran EaCM = C(Eelec + + 3Eelec )l n+2 n 2Ra )l. (14) = C(4Eelec + n+2 Thus, in a round of rotation, the total additional energy cost in a cluster is Eacluster = EaCM + EaCH 2C + 5)Ran ]l. (15) = [(5C + 5)Eelec + ( n+2 There are C + 1 nodes in a cluster; the number of rotation is no more than C +1. Therefore, the total additional energy of the cluster in the whole cluster lifetime is Eacluster = EaCM + EaCH 2C +5)Ran ]l. = (C +1)[(5C +5)Eelec +( n+2 (16) We denote the total rounds of data collection in a cluster as T . Then, we have n+1 (E0i − Eres ) − Eatotal T = i=1 , (17) Etotal where E0i is the initial energy of node i, and Eres is the energy left when the node dies. Considering a node i in a cluster, it can play as cluster head once and cluster member for C times at most. We assume that the additional energy cost while being cluster head is EaCHi , and the additional energy it consumes while being cluster member is EaCMi . Then, the additional energy cost of this node is Eanodei = EaCHi + EaCMi , (18) EaCHi = 5(Eelec + Ran )l + CEelec l (19) = [(C + 5)Eelec + 5Ran ]l, 2Ran + 3Eelec )l EaCMi = C(Eelec + n+2 2Ran = C(4Eelec + )l. (20) n+2 We assume that the rounds of data collection is ti in the
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period that node i is the cluster head. We have Ecuri − Eres n = Eanodei + ECHi + (T − ti ) ECMi j=1,j=i
= Eanodei + (ECHi − ECMi )ti + T ECMi , (21) where ECHi is the energy consumption if node i acts as the cluster head, and ECMi is the energy consumption when node i acts as a member node in a round of data collection: 2Ran )l, (22) ECMi = (Eelec + Esen + n+2 ECH = CEelec l + Esen l + (C + 1)Ecom l +(Eelec + dndoBS )l = [(C + 1)Eelec + Esen +(C + 1)Ecom + dndoBS ]l. (23) ti can be calculated according to the formula (21): Ecuri − Eres − Eanodei − T ECMi ti = . (24) ECHi − ECMi We can find that the optimal expected value of the threshold of node i is (25) Threshold = Ecuri − ECHi ti .
5
EDUC analysis
Analyzing EDUC, we can summarize the characteristics of EDUC as follows: 1) EDUC chooses nodes with high residual energy as the next cluster heads, which can reduce the frequency of cluster head rotation and the energy wasted in cluster head rotation. 2) Formula (4) ensures that the waiting time of each node is less than T1 . Thus, any expected cluster head will broadcast a Head Msg and become a cluster head before T1 expires, which can ensure that all the nodes are covered by the generated cluster heads. There is at most one cluster head in each Rc radio covered range, because different nodes have different waiting times. Therefore, there is one and only one cluster head with in any Rc area. The cluster heads are distributed well. 3) Nodes use uneven competition ranges to construct clusters of uneven sizes. Thus, the energy consumption among nodes is balanced. 4) EDUC adopts an energy-driven cluster head rotation strategy. Each node having up to an opportunity to be cluster head minimizes the additional cost as well as the number of cluster head rotation. Here, we will analyze the energy efficiency η of EDUC. In EDAC, η the proportion of the effective energy cost in the total energy cost: Ee Ee = , (26) η= Et E e + Ea where Ee is effective energy cost, and Ea is additional energy cost. In EDUC, each node acts as cluster head not more than once. Therefore, the additional energy cost of the network during the whole network lifetime is (27) Ea = N Eanode . Compared with time-driven algorithms, EDUC has a smaller additional cost and achieves a higher value η. Furthermore, EDUC localizes the topology construction and avoids the phenomenon of interrupted network func-
tion caused by global topology reconstruction that happens in time-driven algorithms. Here, we give an analysis of parameters involved in this algorithm. In formula (5), the size of clusters is determined by Rmax and α, the larger Rmax is, the lager RCi will be. Correspondingly, the cluster size will be larger. The value of α determines the equality level of the cluster size. The larger α is, the more uneven the size will be. Analyzing formula (5), we can see that the clusters farther away from the BS have smaller sizes than those closer to the BS, thus, the cluster heads father away from the BS can preserve some energy for long-distance data transmission. In formula (7), priority pi is determined by the residual energy and distance to the cluster head of node i. β means who is more important. Here, β is in [0.5, 1], which means that the primary probability is the residual of node, and the subsidiary probability is the distance to the cluster head. We choose the node with the highest p to ensure that the new cluster heads have enough energy and to avoid the edge positions in the clusters.
6 Simulations The simulation was performed in NS-2, and two scenarios were chosen: Sparse scenario There were 100 nodes randomly deployed over a 200 m×200 m field. Dense scenario 400 There were nodes randomly deployed over a 200 m×200 m field. The parameters of simulations are listed in Table 2. Table 2 Parameters of simulations. Parameter
Value
Sensor field BS location Number of nodes EiniNon Data packet size Eelec fs mp Esen Ecom
200 m×200 m (250, 100) 100,400 1∼3 J 500 bytes 50 nJ/bit 10 pJ/(bit·m2 ) 0.0013 pJ/(bit·m4 ) 0 J/bit 5 nJ/(bit·signal)
Fig. 2 shows the topology of these two scenarios.
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Fig. 2 Sparse network and dense network.
We run EDUC in these scenarios, respectively. Fig. 3 shows the relationship between the number of cluster heads and Rmax when α chooses different values. As shown in Fig. 3, the curves of α = 0.5 are higher than that of α = 0. The reason is that, when Rmax is fixed, the increase of α leads to the decrease of cluster radius. Furthermore, the value of the curves in Fig. 3 are approximate, which means that the number of cluster heads is determined by Rmax and α. The number of nodes in the network has little effect on the number of clusters. Fig. 4 Relationship between Rmax and network lifetime.
To measure the network lifetime generated by our new protocol and others, we run LEACH, HEED [2], and EDUC. Fig. 5 shows the comparison of these three protocols in terms of network lifetime.
Fig. 5 Network lifetime.
Fig. 3 Number of cluster heads generated.
There is no clear definition on network lifetime. Here, we define the network lifetime as percentage node alive (PNA) [5]. The network lifetime is defined as the time when 90 percent of nodes are alive. In the two scenarios, we set α = 0.5 and run EDUC. Fig. 4 shows the relation between Rmax and network lifetime. As can be seen in Fig. 4, the network lifetime of dense network is a little longer than that of sparse network, which means that increasing the number of nodes will prolong the network lifetime and the increase is not obvious. An other information shown in Fig. 4 is that the most appropriate Rmax is 120∼140 for the sparse scenario and 90∼110 for the dense scenario.
Compared with LEACH and HEED, EDUC can prolong the network lifetime. Furthermore, the network lifetime of intensive network is slightly longer than that of sparse network in EDUC. However, in the other two protocols, there is a slight decrease.
7 Conclusions An energy-driven clustering algorithm named EDUC is proposed in this paper. In EDUC, cluster heads use uneven competition ranges to construct clusters of uneven sizes. Clusters farther away from the BS has smaller sizes in order to preserve some energy for long-distance data transmission. Therefore, the energy consumption among cluster heads is balanced effectively. Based on this clustering structure, an energy-driven cluster head rotation scheme is proposed to minimize the unnecessary energy waste. Each node
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acts as cluster head no more than once during the whole network lifetime. Thus, EDUC minimizes the additional cost and achieves high energy efficiency. In this paper, we accurately compute the energy threshold in cluster head rotation based on the assumption that the cluster head is a single-hop away from the BS. However, the single-hop assumption may not always be appropriate for some real situation. In clustering multihop networks using a random competition scheme for electing cluster head, the number of packages forwarded by a cluster head is not easy to estimate while computing the energy threshold. Therefore, the energy-driven cluster head rotation scheme proposed here is not appropriate for multihop networks, because the energy threshold is asked to be very precise. For further work, we will focus on the application of EDUC to multihop wireless sensor networks. References [1] W. R. Heinzelman, A. Chandrakasan, H. Balakrishnan. Energyefficient communication protocol for wireless microsensor networks[C]//Proceedings of the 33rd Annual Hawaii International Conference on System Sciences. Maui, HI, 2000: 1 – 10. [2] O. Younis, S. Fahmy. HEED: A hybrid, energy-efficient, distributed clustering approach for Ad hoc sensor networks[J]. IEEE Transactions on Mobile Computing, 2004, 3(4): 366 – 379. [3] M. Liu, J. Cao, G. Chen, et al. EADEEG: An energy-aware data gathering protocol for wireless sensor networks[J]. Journal of Software, 2007, 18(5): 1092 – 1109. [4] C. Li, M. Ye, G. Chen, et al. An energy-efficient unequal clustering mechanism for wireless sensor networks[C]//Proceedings of the IEEE International Conference on Mobile Adhoc and Sensor Systems Conference. Washington, 2005: 597 – 604. [5] X. Zhou, M. Wu, J. Xu. BPEC: An energy-aware distributed clustering algorithm in WSNs[J]. Journal of Computer Research and Development, 2009, 46(5): 723 – 730. [6] Y. Wang, Q. Zhao, D. Zheng. Energy-driven adaptive clustering data collection protocol in wireless sensor networks[C]//Proceedings of the International Conference on Intelligent Mechatronics and Automation. New York: IEEE, 2004: 599 – 604. [7] S. Gamwarige, E. Kulasekere. An algorithm for energy driven cluster head rotation in a distributed wireless sensor network[C]// Proceedings of the International Conference on Information and Automation. New York: ACM, 2005: 354 – 359. [8] Y. Wu, Z. Chen, Q. Jing, et al. LENO: LEast rotation nearoptimal cluster head rotation strategy in wireless sensor networks[C]// Proceedings of the 21st International Conference on Advanced Networking and Applications. Los Alamitos: IEEE Computer Society, 2007: 195 – 201. [9] H. Huang, J. Shen. An energy-driven adaptive cluster head rotation alforithm for wireless sensor networks[J]. Journal of Electronics & Information Technology, 2009, 31(5): 1040 – 1044. [10] M. Perillo, C. Zhao, W. R. Heinzelman. An analysis of strategies for mitigating the sensor network hot spot problem[C]//Proceedings of
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thd 2nd Annual International Conference on Mobile and Ubiquitous Systems: Networking and Services. Los Alamitos: IEEE Computer Society, 2005: 474 – 478. [11] X. Wu, G. Chen. The energy hole problem of nonuniform node distribution in wireless sensor networks[J]. Chinese Journal of Computer, 2008, 31(2): 1 – 9. [12] S. Soro, W. R. Heinzelman. Prolonging the lifetime of wireless sensor networks via unequal clustering[C]//Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium. Los Alamitos: IEEE Computer Society, 2005: 236 – 243. [13] M. Xiang. Energy efficient clustering algorithm for maximizing lifetime of wireless sensor networks[J]. Aeu-International Journal of Electronics and Communications, 2010, 64(4): 289 – 298. [14] S. Gamwarige, E. Kulasekere. Performance analysis of the EDCR algorithm in a distributed wireless sensor network[C]//Proceedings of the International Conference on Wireless and Optical Communication Networks. New York: IEEE, 2006: 85 – 89. [15] S. Gamwarige, E. Kulasekere. Application of the EDCR algorithm in a cluster based multi-hop wireless sensor network[C]//Proceedings of the International Symposium on Communications and Information Technologies. New York: IEEE, 2006: 303 – 308. Jiguo YU received his Ph.D. degree in Operational Research and Control Theory from Shandong University, Shandong, China, in 2004. He is currently a professor in the School of Computer Science, Qufu Normal University, Shandong, China. His main research interests include wireless networks, algorithms, peer-to-peer computing and graph theory. In particular, he is interested in designing and analyzing algorithms for many computationally hard problems in computer networks. He is a member of the IEEE, and a senior member of the CCF (China Computer Federation). E-mail:
[email protected]. Yingying QI received her B.S. degree in Computer Science and Technology from Qufu Normal University, Shandong, China, in 2008. She is currently a postgraduate in the School of Computer Science, Qufu Normal University. Her main research interest is wireless sensor networks. E-mail: qyy
[email protected].
Guanghui WANG received his Ph.D. degree in Computer and Information Science, at Paris sud University, France, and Ph.D degree in Mathematics, at Shandong University, China, in 2007. During 20082009, he was a postdoctoral fellow in Applied Mathematics and Systems Department at Central School of Paris, France. He is now working in the School of Mathematics, Shandong University, Shandong, China. His research interests include graph theory, combinatorics, algorithms and bioinformatics. He is a reviewer for Mathematics Review, and also is invited to be a reviewer for Discrete Applied Mathematics and the Electronic Journal of Combinatorics. E-mail:
[email protected].
