head is re-elected if its current energy level is below2. Related Works the average value. There’re many researches about network clusteringto reduce energy consumption and prolong network 3. The Proposed Clustering Algorithmlifetime in wireless sensor network in recent years. In this section, first network model is given, and Heinzilman et al.  proposed Low-Energy then our proposed cell based clustering algorithm isAdaptive Clustering Hierarchy (LEACH), which is a described.self-organizing, adaptive clustering protocol utilizing 3.1. Network Modelrandomization to evenly spread work load among Consider a wireless sensor network consisting of anodes in the network. In cluster set-up phase, each large number of sensor nodes which is dispersed on anode elects itself to be a cluster head with a certain rectangular field. Let l and w denote the length and theprobability. Then each non-cluster head node joins a width of the rectangular field respectively. We assumecluster by choosing the cluster head that requires the the following properties about the sensor networkminimum communication energy. Non-cluster head model:node can turn off its radio except during its (1) Sensor nodes are evenly distributed in the targettransmitting time. Each cluster head aggregates data field. Once deployed, all sensor nodes are static.from members and transmits the compressed data to (2) All sensor nodes have same capabilities ofthe data sink directly. Since the cluster head may be far sensing, processing and communication.away from the data sink, it will cost high energy. (3) The transmission range of all sensor nodes is same and fixed which’s denoted by R. Two sensor r nodes can communicate with each other if their distance is less than R. (4) Each sensor node knows its location information r which can be provided by GPS or other location systems. 3.2. Cell Based Clustering Algorithm r First we discuss how to group sensor nodes into clusters. Similar to GAF, the target field is divided into r r r r small non-overlapping “virtual cells” which is a regular hexagon. Sensor nodes belonging to the same Figure 1 Example of virtual grid in GAF cell form a cluster. Without loss of generality, we Xu et al.  presented a Geographical Adaptive assume l≥w. To minimize the total number of clusters,Fidelity (GAF) algorithm. As depicted in figure 1, the we partition the rectangle into cells by way aswhole area where nodes are distributed is divided into illustrated in figure 2. The cells are arranged in array.small “virtual grids”. Each node uses its location Each cell is identified with a two-tuples (i,j), where i isinformation which can be provided by GPS or other the row order of the array and j is the column order oflocation systems to determine which grid it belongs to. the array. Let Ci,j denotes the cell whose identificationNodes belonging to the same grid form a cluster. Each is (i,j). To ensure cluster head can relay data fromnode in a cluster has opportunity to be selected as adjacent cell, it’s required that any node in adjacentcluster head. To ensure cluster head can relay data cell can communicate with each other. The maximumbetween clusters, it’s required that any node in adjacent distance between any two nodes in adjacent cell isgrid can communicate with each other. Let R denote marked in figure 2. Let R denote the transmissionthe transmission range of sensor node and r denote the range of sensor node and r denote the radius of thesize length of virtual grid. Therefore r≤R/ 5 must be circumcircle of cell. Therefore, we get:held. r2+(2 3 r)2≤R2 (1) Moussaoui et al.  presented a centralized Then r≤R/ 13 . In fact, we set r=R/ 13 to reduce theclustering algorithm. Sensor nodes are organized into total number of clusters.no overlapping clusters by taking into account acombined effect of the cluster size, transmission powerand energy levels of nodes. Each node cancommunicate with any other node in a cluster. Once allclusters are set up, they don’t change in order to reducethe computation and communication costs. Cluster 183Authorized licensed use limited to: Jeppiaar Engineering College. Downloaded on July 19,2010 at 15:20:45 UTC from IEEE Xplore. Restrictions apply.
balance energy of each node within cluster, it’s 4,0 4,1 4,2 4,3 4,4 4,5 important to elect the node with the maximum energy to be cluster head. On the other hand, the energy of 3,0 3,1 3,2 3,3 3,4 3,5 3,6 each node will dynamically decrease as the time elapses, so the cluster head must be re-elected u periodically. Here we give a low-cost local algorithm 2,0 2,1 2,2 v 2,3 2,4 2,5 w for electing cluster head, which is described as follows: (1) If a node finds there’s no cluster head, it set a 1,0 1,1 1,2 R 1,3 1,4 1,5 1,6 timer which is in inverse proportion to its energy. If no r cluster head is elected before the timer fires, it elects 0,0 0,1 0,2 0,3 0,4 0,5 itself to be cluster head. (2) If a node finds its energy is more than twice the l energy of current cluster head, it elect itself to be new cluster head replacing current cluster head. Figure 2 Partitioning the rectangle into virtual Because each cluster member can directly cells communicate with the cluster head, intra-cluster According to location information, each node can communication is sample. Subsequently we discussdetermine which cell it belongs to without exchanging inter-cluster communication. Assume only adjacentmessage with each other. Assume the origin is the left cell can directly communicate with each other due todown corner of the rectangle, the coordinate of the restriction of MAC protocol. Let (si,sj) and (di,dj)node is (x,y), the identification of the cell in which the denote the identification of the source cell and thenode is located is (i,j). The value of (i,j) can be destination cell respectively. The question is how tocalculated from (x,y) by the following procedure: establish the communication path connecting Csi,sj and Procedure Cal_Cell_ID Cdi,dj. As illustrated in figure 2, we first route vertically Input: x, y, r to the cell which has the same row order as the Output: i, j destination cell while try to reduce the column i= ⎣ y / (3 / 2r )⎦ ; difference, then route horizontally to the destination if (i%2=0) cell. Let Cci,cj denote the current cell and Cni,nj denote j= ⎣x / ( 3r )⎦ ; the next routing cell. The value of (ni,nj) can be u=x-j× 3 r; calculated by the following procedure: else Procedure Route j= ⎣x / ( ) 3 r + 0 .5 ⎦; Input: di, dj, ci, cj Output: ni, nj u=x-(j-0.5)× 3 r; if (di=ci) v=y-i×3/2r; ni=ci; if (v>r) if (dj<cj) v=v-r; nj=cj-1; if (u< 3 v) else if (i%2=1) nj=cj+1; j--; else i++; if (di<ci) else if (u> 3 r- 3 v) ni=ci-1; else if (i%2=0) ni=ci+1; j++; if (ci%2=1 and dj<cj) i++; nj=cj-1; return (i, j); else if (ci%2=0 and dj>cj) nj=cj+1; Figure 3 Procedure of calculating cell else nj=cj; identification from coordinate of node return (ni, nj); After the clustering procedure, all nodes aregrouped into clusters. Each node belongs to only one Figure 4 Procedure of routing between clusterscluster. Then a cluster head must be elected from the It’s easy to see that the above routing procedure cannodes set in each cluster. Cluster head perform more always produce the optimal communication pathfunctions than non-cluster head nodes and can’t go to between the source cluster and the dentition cluster ifsleep, consequently it will consume more energy. To measured by the hops of the communication path. 184Authorized licensed use limited to: Jeppiaar Engineering College. Downloaded on July 19,2010 at 15:20:45 UTC from IEEE Xplore. Restrictions apply.
⎡ 5l ⎤ ⎡ 5 w ⎤4. Performance Evaluation LPGAF= ⎢ ⎥+⎢ ⎥−2 (5) ⎢ R ⎥ ⎢ R ⎥ In this section, we evaluate the performance of ourCBC algorithm with comparing to GAF algorithm For CBC algorithm, if the number of rows is even,presented in . The measurements include the the identification of the cell at right up corner isnumber of clusters, the length of inter-cluster ( ⎡2 w /(3r ) + 1 / 3⎤ -1, ⎡l /( 3r ) + 0.5⎤ -1). Otherwise thecommunication path, and the network lifetime. identification is ( ⎡2 w /(3r ) + 1 / 3⎤ -1, ⎡l /( 3r )⎤ -1). So the First we analyze the number of clusters generated largest length of inter-cluster communication path ofby CBC algorithm and GAF algorithm respectively. CBC algorithm which’s denoted by LPCBC can beThe smaller the number of clusters, the more energy is obtained as follows:saved because the more nodes can go to sleep. The ⎧⎡ l 1 ⎤ ⎡ 2w 1 ⎤ ⎡ 2w 1 ⎤number of clusters by GAF algorithm which’s denoted ⎪⎢ + ⎥+⎢ + ⎥ /2−2 ⎢ 3r + 3 ⎥ is evenby CNGAF can be easily obtained as follows: ⎪⎢ 3r 2 ⎥ ⎢ 3r 3 ⎥ ⎢ ⎥ LPCBC= ⎨ , ⎡ l ⎤ ⎡ w ⎤ ⎡ 5l ⎤ ⎡ 5 w ⎤ ⎪⎡ l ⎤ ⎡ 2w 1 ⎤ 3 ⎡ 2w 1 ⎤ CNGAF= ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥⎢ ⎥ (2) ⎪⎢ ⎥+⎢ + /2− ⎢ 3r + 3 ⎥ is odd ⎢ r ⎥⎢ r ⎥ ⎢ R ⎥⎢ R ⎥ ⎩⎢ 3r ⎥ ⎢ 3r 3 ⎥ ⎥ 2 ⎢ ⎥ For CBC algorithm, the cell number of each even where r=R/ 13 (6)row is ⎡l /( 3r )⎤ , the cell number of each odd row We can compute the asymptotic value ofis ⎡l /( 3r ) + 0.5⎤ , and the total row number is LPCBC/LPGAF when the target field is large enough as follows: ⎡2w /(3r ) + 1 / 3⎤ . So the number of clusters by CBC 13l 13walgorithm which’s denoted by CNCBC can be obtained +as follows: LPCBC 3R 3R 39l + 13 w lim = lim = (7) ⎧⎛ ⎡ l →∞ , w→ ∞ LPGAF l →∞ , w →∞ 5l 5w 45l + 45 w l ⎤ ⎡ l 1 ⎤ ⎞⎡ 2w 1 ⎤ + ⎪⎜ ⎢ ⎥+⎢ + ⎥ ⎟⎢ + ⎥/2 R R ⎪⎜ ⎢ ⎝ 3r ⎥ ⎢ 3r 2 ⎥ ⎟ ⎢ 3r 3 ⎥ ⎠ ⎪ 25 ⎪ ⎡ 2w 1 ⎤ ⎪ when ⎢ + ⎥ is even CBC ⎪ ⎢ 3r 3 ⎥CNCBC= ⎨ , 20 GAF The average length ⎪⎛ ⎡ l ⎤ ⎡ l 1 ⎤ ⎞⎛ ⎡ 2 w 1 ⎤ ⎞ ⎡ l ⎤ ⎪⎜ ⎢ ⎜ ⎥+⎢ + ⎥ ⎟⎜ ⎢ ⎜ 3r + 3 ⎥ − 1⎟ / 2 + ⎢ ⎟ ⎥ ⎪⎝ ⎢ 3 r ⎥ ⎢ 3 r 2 ⎥ ⎟⎝ ⎢ ⎠ ⎥ ⎠ ⎢ 3r ⎥ 15 ⎪ ⎪ ⎡ 2w 1 ⎤ when ⎢ + ⎥ is odd 10 ⎪ ⎩ ⎢ 3r 3 ⎥ where r=R/ 13 (3) 5 We can compute the asymptotic value ofCNCBC/CNGAF when the target field is large enough as 0follows: 5 6 7 8 9 10 11 12 13 14 15 13l ⎛ 2 13 w 1 ⎞ The width of the rectangle (102m) ⎜ + ⎟ CN CBC 3 R ⎜ 3R ⎝ 3⎟⎠ 676 Figure 5 The average length of inter-cluster lim = lim = (4) communication path for different shape of l → ∞ , w → ∞ CN GAF l →∞ , w →∞ 5l 5w 675 rectangles R R From above we can see LPCBC<LPGAF. In the special So the number of clusters generated by CBC case of l=w, the ratio is about 0.734. Subsequently wealgorithm is approximately equal to GAF algorithm. analyze the average length of inter-cluster Next we analyze the length of inter-cluster communication path of CBC algorithm and GAFcommunication path of CBC algorithm and GAF algorithm by simulation. The transmission range ofalgorithm respectively. The shorter the length of inter- node is set to be R=100m. The length of the targetcluster communication path, the more energy is saved. rectangle is set to be l=1500m. The width of the targetThe longest inter-cluster communication path of GAF rectangle w is varied from 500m to 1500m. Figure 5algorithm is the communication path between the grid shows the average length of inter-clusterat left down corner and the grid at right up corner. Let communication path of CBC algorithm and GAFLPGAF denote it length, which can be obtained as algorithm for different shape of rectangles. It can befollows: seen that the average length of inter-cluster 185Authorized licensed use limited to: Jeppiaar Engineering College. Downloaded on July 19,2010 at 15:20:45 UTC from IEEE Xplore. Restrictions apply.
communication path of CBC algorithm is smaller than regular hexagon. Sensor nodes belonging to the sameGAF algorithm in all cases. When the target region is a cell form a cluster. The size of cells is selected to besquare, it’s about 78.6% of GAF algorithm. The ratio R/ 13 so that any node in adjacent cell canof CBC algorithm to GAF algorithm is about 79.4% on communicate with each other, where R is theaverage. transmission range of sensor node. We present an 140 algorithm of calculating which cell a sensor node belongs to from its coordinate. We also present a low- CBC The network lifetime (day) 120 cost local algorithm for electing cluster head. And we GAF 100 give a method of routing that can produce the optimal inter-cluster communication path. 80 We evaluate the performance of our proposed CBC 60 algorithm with comparing to GAF algorithm. By analysis, the numbers of clusters generated by CBC 40 algorithm and GAF algorithm are approximately equal, 20 but the largest length of inter-cluster communication path of CBC algorithm can reach 73.4% of that of 0 GAF algorithm at most. Simulation results show that 4 5 6 7 8 9 10 the ratio of the average length of inter-cluster The number of sensor nodes (103) communication path of CBC algorithm to that of GAF Figure 6 The network lifetime for different algorithm is 79.4% on average, and the network number of sensor nodes lifetime by CBC algorithm can be prolonged by about Finally we compare the network lifetime by CBC 10% with comparison to GAF algorithm.algorithm with GAF algorithm by simulation. Thetransmission range of node is set to be R=100m. The 6. Acknowledgementtarget rectangle is set to 1000×1000m2. The number of This paper was supported by Guangdong Naturalsensor nodes is varied from 4000 to 10000. The battery Science Foundation (2008254), Science Foundation forpackage of sensor nodes can supply 2200mAh at 3V, so Youths of Shenzhen University (200869), Nationalinitial energy of each node is 23.76kJ. We use the radio Science Foundation of China (60602066), Foundationmodel described in : The radio spends 200nJ/bit to of Shenzhen City (JC200903120069A andtransmit 1-bit and spends 100nJ/bit to receive 1-bit SG200810220145A).over a transmission range of 100m. Communications inthe network obey the Poisson process and the average 7. Referencesnumber of communications per unit time is 10s-1. The  I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, E.source and dentition of a communication are random Cayirci. Wireless sensor networks: a survey. Computerpoints in the rectangle. The average data volume of a Networks, 2002, 38(4): 393-422.communication is 10KB. The average power of node  Y. Tian, E. Ekici. Cross-layer collaborative in-networknot in radio is 2mW. The average power of non-cluster processing in multihop wireless sensor networks. IEEEhead node in idle-listening is 10mW. The network Transactions on Mobile Computing, 2007, 6(3): 297-lifetime is defined as from beginning to the time when 310.data successfully routing rate drops below 85% .  H.-M. Seo, Y. Moon, Y.-K. Park, D. Kim, D.-S. Kim, Y.-S. Lee, K.-H. Won, S.-D. Kim, P. Choi. A low powerFigure 6 shows the network lifetime changes with fully CMOS integrated RF transceiver IC for wirelessdifferent numbers of nodes by CBC algorithm and sensor networks. IEEE Transactions on Very LargeGAF algorithm. It can be seen that the network lifetime Scale Integration Systems, 2007, 15(2): 227-231.increases with the increasing of the number of nodes  M.A. Lopez-Gomez, J.C. Tejero-Calado. A lightweightby both algorithms. But when the number of node is and energy-efficient architecture for wireless sensorsame, the network lifetime by CBC algorithm is longer networks. IEEE Transactions on Consumer Electronics,than GAF algorithm because the average 2009, 55(3): 1408-1416.communication path of CBC algorithm is shorter. On  W. Li, C.G. Cassandras. A minimum-power wirelessaverage it’s about 1.1 times of GAF algorithm. sensor network self-deployment scheme. In Proceedings of 2005 IEEE Wireless Communications and Networking Conference, 2005: 1897-1902.5. Conclusions  D. Estrin, R. Govindan, J. Heidemann, S. Kumar. Next In this paper we propose a cell base clustering century challenges: scalable coordination in sensoralgorithm (CBC algorithm). The target field is divided networks. In Proceedings of the ACM/IEEEinto small non-overlapping “virtual cells” which is a International Conference on Mobile Computing and Networking, 1999: 263-270. 186Authorized licensed use limited to: Jeppiaar Engineering College. Downloaded on July 19,2010 at 15:20:45 UTC from IEEE Xplore. Restrictions apply.
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