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Relay Node Placement for Multi-Path Connectivity in Heterogeneous Wireless Sensor Networks
Available online at www.sciencedirect.com
Procedia Technology 4 (2012) 732 – 736
C3IT-2012
Relay Node Placement for Multi-Path Connectivity in Heterogeneous Wireless Sensor Networks Deepak R Dandekara, Dr. P.R.Deshmukhb a
B.D.College of Engineering, Sevagram, Wardha, M.S., India b Sipna Engineering College, Amravati, M.S., India
Abstract In this paper, we study the problem of deploying additional relay nodes to provide multi-path connectivity (kconnectivity) between all nodes in wireless sensor network. Specifically given a disconnected wireless network, few additional nodes is to be deployed so that the augmented network will have higher degree of connectivity for fault tolerance. We propose an algorithm based on Particle Swarm Optimization, that places optimum number of energy constrain relay nodes to achieve desired connectivity between heterogeneous wireless sensor nodes in which the communication range of each sensor node is different. In simulation, the proposed algorithm is compared with the heuristic algorithm for number of relay nodes required to obtain desired k-connectivity and the average value degree of nodes in resulting network. Result shows that Particle Swarm Optimization based algorithm perform over heuristic algorithm.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of C3IT Keywords: Wireless sensor networks, relay nodes, K-connectivity, particle swarm optimization
1. Introduction In real applications of Wireless Sensor Networks (WSNs), unpredictable events such as energy depletion and harsh environmental factors may cause the wireless nodes to fail and partition the network. The basic requirement in such applications is the network required to be k-connected, that is, to have k node disjoint paths between every pair of nodes in the network, which is also referred as multi-path connectivity. The multi-path connectivity may be used for different purposes including fault-tolerance, i.e., being able to maintain operation in a timely manner with the occurrence of failures, and high throughput through multi-path routing. Usually k-connectivity in a network can be established with placing the minimum number of additional nodes, referred as relay nodes. Optimal relay node placement
2212-0173 © 2012 Published by Elsevier Ltd. doi:10.1016/j.protcy.2012.05.119
Deepak R Dandekar and P.R. Deshmukh / Procedia Technology 4 (2012) 732 – 736
is a very challenging problem that has been proven to be NP-Hard [1]. To tackle this problem, several heuristics have been proposed to find sub-optimal solutions [2], [3], [4], [5]. In [6] authors tried to deploy a minimum number of relay nodes so that, every sensor node can directly communicate with at least two relay nodes and the backbone network consisting only of relay nodes that has 2-connectivity. Hisham M. Almasaeid et al. [7] proposed a hybrid algorithm which considers the communication ranges by exploiting intersection regions needed to repair k-connectivity to reduce the number of additional nodes in a wireless sensor network. In [8] Quanhong Wang et al. formulated a generalized node placement optimization problem aimed at minimizing the network cost with constraints on lifetime and connectivity. In [9] authors proposed algorithms for partial and full k-connectivity. A constrained version of relay placement [10] is studied relay placement for heterogeneous and hybrid network. In [11], authors proposed approximation and greedy algorithms based on the minimum kconnected sub-graph. For a more detailed and comprehensive report on the current state of research on the minimum relay node placement problem we refer the reader to the survey in [12]. Optimally deployed WSN assures adequate quality of service, long network life and financial economy [13]. The particle swarm optimization (PSO) has been shown to be effective in optimizing difficult multidimensional discontinuous problems in a variety of fields [14].Available PSO solutions to the deployment problem are computed centrally on a base station for determining positions of sensor and relay nodes discussed in [15]. Our work addresses the problem of maintaining desired k-connectivity between all nodes in multi-hop heterogeneous wireless sensor networks. In this paper, we discuss two offline algorithms which compute the locations of homogeneous relay nodes for desired K-connectivity in wireless sensor networks consist of limited number of heterogeneous sensor nodes. In the first algorithm, concept of steinerization of edges between two degree deficient nodes is used. Result of this algorithm is compared with proposed PSO based algorithm. 2. Network Model and Problem Specification We consider model of stationary heterogeneous multi-hop wireless sensor network that contains n heterogeneous sensor nodes, each mounted with an omni-directional antenna, which can transmit in its coverage area are randomly located in 2D terrain. Formally WSN can be described as a graph G = (V, E), where V is the set of n vertices (sensors nodes) and E is the set of transmission links called edges between pairs of nodes. There is a link from sensor u to sensor v if and only if v is located in u’s transmission range, then v is called neighbor of u. We assume that if all nodes transmit with its maximum power, the topology is not a complete graph and it contains all possible unidirectional/bidirectional links. In the given network, we place the relay nodes so as to achieve desired level of connectivity between the nodes. In this work we study finding the minimum number of relay nodes needed (and their locations) such that the resulting network (including sensor nodes and relay nodes) is set of V’ nodes, k-edge (vertex) connected in the graph G’ = (V’, E’). 3. Algorithms for Relay Node Placement In this Section, we present the two different iterative algorithms that run offline. The placement of additional relay nodes by these algorithms, not only achieves desired connectivity but also have significant impact on other parameters of the network.
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Deepak R Dandekar and P.R. Deshmukh / Procedia Technology 4 (2012) 732 – 736
3.1. Steiner-MPC Algorithm The objective of Steiner-MPC algorithm is to deploy a minimum number of relay nodes to form minimum k-vertex connected network such that in the resulting network, there exist minimum k vertexdisjoint paths from any sensor node to any other sensor node or relay nodes previously deployed. In brief, given a set of nodes V, for nodes u and v having degree value less than k-desired, the algorithm create a path between u and v, placing as few relay nodes as possible, while ignoring all the other sensor nodes and any previously deployed relay nodes. To facilitate creating such paths the algorithm first computes weight W(u,v), such that W(u,v) = 0, if transmission range of u, T(u) > d(u,v) and W(u,v)= ceil( (d(u,v)T(u))/T(r)) if T(u) > d(u,v) and then sort weight vector in ascending order for all nodes in V, then we calculate degree of a node as it equal to number of zeros in weight vector. If degree of u found less than minimum degree specified then for the first w(u,v) > 0 which is minimum in sorted result, place one relay node r on the straight line between u and v such that d(u,r)=T(u) and then, evenly place W(u,v) – 1 relay nodes along the straight line between u and v. In this way, create a path from u to v. This procedure described in algorithm 1, which is near similar to and iterative version of algorithm in H-WSN [2] for steinerization of edges. Algorithm iteratively increases the degree of each node in V to form defined minimum k-vertex connected network. W(u,v)=
{
0 ceil( (d(u,v)-T(u)) / T(r))
if d(u,v) T (u ) if d(u,v) > T (u )
(3)
Algorithm 1: Steiner-MPC Input: G( V), integer k Output: Set of relay nodes R. 1: R := I (empty set); 2: G’ := ( V ); 3: while G’ I for each edge (u,v) do 4: 5: d(u,v) := { | uv | ; u,v V }; 6: Compute weight of each edge (u,v) according to Equation 3; 7: end for 8: G := ( V R, W ); 9: Draw a spanning graph G; 10: Compute degree of each Vertex and derive G’ such that it consist of nodes having degree less than required k value; 11: Steinerize edge between first node u and its nearest node v in G’ by placing relay nodes and add relay nodes into R; 12: end while 13: Output R; 3.2. PSO-MPC Algorithm The initial steps of this algorithm is identical to steps 1 to 8 of Steiner-MPC algorithm, in which we first computes sorted weight W(u,v) vectors for all nodes in V and its degree which is equal to the number of zeros in weight vector. The list of nodes having degree value less than desired is created and PSO algorithm is called. PSO is a population based iterative parallel search algorithm that models social behaviour and movement dynamics of swarm [16]. The PSO algorithm uses a simple concept is easy to
Deepak R Dandekar and P.R. Deshmukh / Procedia Technology 4 (2012) 732 – 736
implement and is computationally efficient. The PSO runs for each degree deficient node in the list to place a relay node with the objective of particle swarm population to minimize sum of weights all nodes in the list with newly placed relay and to increase connectivity of maximum nodes in the list. This procedure repeated until the list is vacant and all target nodes attains minimum desired k-connectivity. 4. Experimental Results The algorithms described in section 3 are implemented and simulated in Matlab. Sensor nodes having different communication ranges are randomly deployed in a 1000m x 1000m, 2D terrain. Transmission range of sensor nodes are randomly chosen from the set {50 100 150 200}. The transmission ranges of all relay nodes are assumed to be same and set it to 200m. The parameters for PSO algorithm are set as c1=1.2, c2= 0.12, and w = 0.9. The numbers of particles used in PSO algorithms is 50. The simulation is performed for both the algorithms with two different values of k. In first set of simulation, we have used k=2 and then increased number of sensor nodes from 5 to 100. In each simulation the number of relay nodes and average degree of nodes are computed. Then the procedure is repeated for k=3. The cost per node defined as the ratio of number of relay nodes to the number of sensor nodes and connectivity improvement defined as a ratio of average degree value provided by resultant minimum k-vertex graph to number of relay nodes placed are shown in fig. 3 and 4 respectively.
Fig. 1. Relay nodes Vs. Sensor nodes for K=2
Fig. 3. Connectivity Improvement Vs. Sensor nodes
Fig. 2. . Relay nodes Vs. Sensor nodes for K=3
Fig. 4. Relay Cost Vs. Sensor nodes
In performances shown in Fig 1, and 2, we observe initially for smaller number of sensor nodes, the relay nodes placed by PSO-MPC algorithm are in greater number than that of Steiner-MPC. Later as number of sensor nodes increases, the relay nodes placed by PSO-MPC algorithm are goes on decreasing sharply as compared to Steiner-MPC algorithm. With the results, we can easily conclude that, for large scale
735
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Deepak R Dandekar and P.R. Deshmukh / Procedia Technology 4 (2012) 732 – 736
wireless sensor networks, PSO based method provides optimal solutions and better than Steiner based method under the same network parameter setting, no matter k=2 or 3. Results shown in fig 3 indicate that PSO-MPC algorithm is ahead of Steiner-MPC in concern to network connectivity improvement and cost of relays placed for desired connectivity. 5. Conclusion and Future Work In this work we proposed an algorithm for deploying minimum additional relay nodes to provide multi-path connectivity (k-connectivity) in heterogeneous wireless sensor networks. The algorithm uses swarm intelligence in placing the relay nodes optimally. Performance comparison showed that PSO-MPC perform well over Steiner-MPC. Proposed PSO based algorithm is iterative algorithm which uses lower number of relay nodes deployed to attain desired k-connectivity in given wireless sensor network. The PSO-MPC requires high computational time than Steiner-MPC and it increases with increase in swam population. In future, we would like to conduct similar experiments to find the optimal number of heterogeneous relay node to be placed (relay nodes with different transmission capabilities) for desired kconnectivity in heterogeneous wireless sensor networks. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
Mohamed Younis, Kamal Akkaya, Strategies and Techniques for Node Placement in Wireless Sensor Networks: A Survey. Journal of Ad Hoc Networks Elsevier 6(4) 2008. Xiaofeng Han, Xiang Cao, Errol L. Lloyd, and Chien-Chung Shen: Fault-Tolerant Relay Node Placement in Heterogeneous Wireless Sensor Networks. IEEE Transactions On Mobile Computing, 9(5) May 2010. A. Kashyap, S. Khuller, and M. Shayman: Relay Placement for Higher Order Connectivity in Wireless Sensor Networks. INFOCOM 1-12 Apr 2006. E.L. Lloyd and G. Xue: Relay Node Placement in Wireless Sensor Networks. IEEE Trans. Computers 56(1) Jan. 2007. X. Cheng, D. Du, L. Wang, and B. Xu, Relay Sensor Placement in Wireless Sensor Networks. Journal of Wireless Networks 14(3) June 2008 347-355. Bin Hao,Han Tang,Guoliang Xue, Fault-tolerant relay node placement in wireless sensor networks: formulation and approximation. Proc. IEEE, Workshop on High Performance Switching and Routing 2004 246 – 250. Hisham M. Almasaeid and Ahmed E. Kamal, On the Minimum k-Connectivity Repair in Wireless Sensor Networks. IEEE International Conference on Communication 2009 1-5. Quanhong Wang, Kenan Xu, Glen Takahara and Hossam Hassanein, Device Placement for Heterogeneous Wireless Sensor. Networks: Minimum Cost with Lifetime Constraints. IEEE Transactions On Wireless Communications, Vol. 6(7) July 2007. Juhua Pu, Zhang Xiong, Xiaofeng Lu, Fault-tolerant deployment with k-connectivity and partial k-connectivity in sensor. networks. Journal Wireless Communications and Mobile Computing 9(7), July 2009. Misra, S, Seung Don Hong, Guoliang Xue, Jian Tang, Constrained Relay Node Placement in Wireless Sensor Networks: Formulation and Approximations. ACM/IEEE Transaction on Networking, 18(2 ) 2010. Jonathan L. Bredin, Erik D. Demaine, MohammadTaghi Hajiaghayi, Daniela Ru, Deploying Sensor Networks with Guaranteed Capacity and Fault Tolerance. MobiHoc May 25-27 2005. B. Degener, S.P. Fekete, B. Ksempkes and F.M.A.D. Heide, A survey on relay placement with runtime and approximation guarantees. Computer Science-Review 2011 57-68 . Raghavendra V. Kulkarni and Ganesh Kumar Venayagamoorthy, Particle Swarm Optimization in Wireless Sensor Networks: A Brief Survey. IEEE Transaction on Systems, Man, and Cybernetics, Part C: Applications and Reviews 41(2) March 2011. R. C. Eberhart and Y. Shi, “Evolving artificial neural networks, in: Proc.1998 Int. Conf. Neural Networks and Brain, Beijing P.R.C. 1998. J. Hu, J. Song, M. Zhang, and X. Kang: Topology optimization for urban traffic sensor network. Tsinghua Science & Technology 13 Apr 2008. Kennedy, J. and Eberhart, R. C.: Particle swarm optimization in Proc. IEEE international conference on neural networks 1995.
Procedia Technology 4 (2012) 732 – 736
C3IT-2012
Relay Node Placement for Multi-Path Connectivity in Heterogeneous Wireless Sensor Networks Deepak R Dandekara, Dr. P.R.Deshmukhb a
B.D.College of Engineering, Sevagram, Wardha, M.S., India b Sipna Engineering College, Amravati, M.S., India
Abstract In this paper, we study the problem of deploying additional relay nodes to provide multi-path connectivity (kconnectivity) between all nodes in wireless sensor network. Specifically given a disconnected wireless network, few additional nodes is to be deployed so that the augmented network will have higher degree of connectivity for fault tolerance. We propose an algorithm based on Particle Swarm Optimization, that places optimum number of energy constrain relay nodes to achieve desired connectivity between heterogeneous wireless sensor nodes in which the communication range of each sensor node is different. In simulation, the proposed algorithm is compared with the heuristic algorithm for number of relay nodes required to obtain desired k-connectivity and the average value degree of nodes in resulting network. Result shows that Particle Swarm Optimization based algorithm perform over heuristic algorithm.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of C3IT Keywords: Wireless sensor networks, relay nodes, K-connectivity, particle swarm optimization
1. Introduction In real applications of Wireless Sensor Networks (WSNs), unpredictable events such as energy depletion and harsh environmental factors may cause the wireless nodes to fail and partition the network. The basic requirement in such applications is the network required to be k-connected, that is, to have k node disjoint paths between every pair of nodes in the network, which is also referred as multi-path connectivity. The multi-path connectivity may be used for different purposes including fault-tolerance, i.e., being able to maintain operation in a timely manner with the occurrence of failures, and high throughput through multi-path routing. Usually k-connectivity in a network can be established with placing the minimum number of additional nodes, referred as relay nodes. Optimal relay node placement
2212-0173 © 2012 Published by Elsevier Ltd. doi:10.1016/j.protcy.2012.05.119
Deepak R Dandekar and P.R. Deshmukh / Procedia Technology 4 (2012) 732 – 736
is a very challenging problem that has been proven to be NP-Hard [1]. To tackle this problem, several heuristics have been proposed to find sub-optimal solutions [2], [3], [4], [5]. In [6] authors tried to deploy a minimum number of relay nodes so that, every sensor node can directly communicate with at least two relay nodes and the backbone network consisting only of relay nodes that has 2-connectivity. Hisham M. Almasaeid et al. [7] proposed a hybrid algorithm which considers the communication ranges by exploiting intersection regions needed to repair k-connectivity to reduce the number of additional nodes in a wireless sensor network. In [8] Quanhong Wang et al. formulated a generalized node placement optimization problem aimed at minimizing the network cost with constraints on lifetime and connectivity. In [9] authors proposed algorithms for partial and full k-connectivity. A constrained version of relay placement [10] is studied relay placement for heterogeneous and hybrid network. In [11], authors proposed approximation and greedy algorithms based on the minimum kconnected sub-graph. For a more detailed and comprehensive report on the current state of research on the minimum relay node placement problem we refer the reader to the survey in [12]. Optimally deployed WSN assures adequate quality of service, long network life and financial economy [13]. The particle swarm optimization (PSO) has been shown to be effective in optimizing difficult multidimensional discontinuous problems in a variety of fields [14].Available PSO solutions to the deployment problem are computed centrally on a base station for determining positions of sensor and relay nodes discussed in [15]. Our work addresses the problem of maintaining desired k-connectivity between all nodes in multi-hop heterogeneous wireless sensor networks. In this paper, we discuss two offline algorithms which compute the locations of homogeneous relay nodes for desired K-connectivity in wireless sensor networks consist of limited number of heterogeneous sensor nodes. In the first algorithm, concept of steinerization of edges between two degree deficient nodes is used. Result of this algorithm is compared with proposed PSO based algorithm. 2. Network Model and Problem Specification We consider model of stationary heterogeneous multi-hop wireless sensor network that contains n heterogeneous sensor nodes, each mounted with an omni-directional antenna, which can transmit in its coverage area are randomly located in 2D terrain. Formally WSN can be described as a graph G = (V, E), where V is the set of n vertices (sensors nodes) and E is the set of transmission links called edges between pairs of nodes. There is a link from sensor u to sensor v if and only if v is located in u’s transmission range, then v is called neighbor of u. We assume that if all nodes transmit with its maximum power, the topology is not a complete graph and it contains all possible unidirectional/bidirectional links. In the given network, we place the relay nodes so as to achieve desired level of connectivity between the nodes. In this work we study finding the minimum number of relay nodes needed (and their locations) such that the resulting network (including sensor nodes and relay nodes) is set of V’ nodes, k-edge (vertex) connected in the graph G’ = (V’, E’). 3. Algorithms for Relay Node Placement In this Section, we present the two different iterative algorithms that run offline. The placement of additional relay nodes by these algorithms, not only achieves desired connectivity but also have significant impact on other parameters of the network.
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Deepak R Dandekar and P.R. Deshmukh / Procedia Technology 4 (2012) 732 – 736
3.1. Steiner-MPC Algorithm The objective of Steiner-MPC algorithm is to deploy a minimum number of relay nodes to form minimum k-vertex connected network such that in the resulting network, there exist minimum k vertexdisjoint paths from any sensor node to any other sensor node or relay nodes previously deployed. In brief, given a set of nodes V, for nodes u and v having degree value less than k-desired, the algorithm create a path between u and v, placing as few relay nodes as possible, while ignoring all the other sensor nodes and any previously deployed relay nodes. To facilitate creating such paths the algorithm first computes weight W(u,v), such that W(u,v) = 0, if transmission range of u, T(u) > d(u,v) and W(u,v)= ceil( (d(u,v)T(u))/T(r)) if T(u) > d(u,v) and then sort weight vector in ascending order for all nodes in V, then we calculate degree of a node as it equal to number of zeros in weight vector. If degree of u found less than minimum degree specified then for the first w(u,v) > 0 which is minimum in sorted result, place one relay node r on the straight line between u and v such that d(u,r)=T(u) and then, evenly place W(u,v) – 1 relay nodes along the straight line between u and v. In this way, create a path from u to v. This procedure described in algorithm 1, which is near similar to and iterative version of algorithm in H-WSN [2] for steinerization of edges. Algorithm iteratively increases the degree of each node in V to form defined minimum k-vertex connected network. W(u,v)=
{
0 ceil( (d(u,v)-T(u)) / T(r))
if d(u,v) T (u ) if d(u,v) > T (u )
(3)
Algorithm 1: Steiner-MPC Input: G( V), integer k Output: Set of relay nodes R. 1: R := I (empty set); 2: G’ := ( V ); 3: while G’ I for each edge (u,v) do 4: 5: d(u,v) := { | uv | ; u,v V }; 6: Compute weight of each edge (u,v) according to Equation 3; 7: end for 8: G := ( V R, W ); 9: Draw a spanning graph G; 10: Compute degree of each Vertex and derive G’ such that it consist of nodes having degree less than required k value; 11: Steinerize edge between first node u and its nearest node v in G’ by placing relay nodes and add relay nodes into R; 12: end while 13: Output R; 3.2. PSO-MPC Algorithm The initial steps of this algorithm is identical to steps 1 to 8 of Steiner-MPC algorithm, in which we first computes sorted weight W(u,v) vectors for all nodes in V and its degree which is equal to the number of zeros in weight vector. The list of nodes having degree value less than desired is created and PSO algorithm is called. PSO is a population based iterative parallel search algorithm that models social behaviour and movement dynamics of swarm [16]. The PSO algorithm uses a simple concept is easy to
Deepak R Dandekar and P.R. Deshmukh / Procedia Technology 4 (2012) 732 – 736
implement and is computationally efficient. The PSO runs for each degree deficient node in the list to place a relay node with the objective of particle swarm population to minimize sum of weights all nodes in the list with newly placed relay and to increase connectivity of maximum nodes in the list. This procedure repeated until the list is vacant and all target nodes attains minimum desired k-connectivity. 4. Experimental Results The algorithms described in section 3 are implemented and simulated in Matlab. Sensor nodes having different communication ranges are randomly deployed in a 1000m x 1000m, 2D terrain. Transmission range of sensor nodes are randomly chosen from the set {50 100 150 200}. The transmission ranges of all relay nodes are assumed to be same and set it to 200m. The parameters for PSO algorithm are set as c1=1.2, c2= 0.12, and w = 0.9. The numbers of particles used in PSO algorithms is 50. The simulation is performed for both the algorithms with two different values of k. In first set of simulation, we have used k=2 and then increased number of sensor nodes from 5 to 100. In each simulation the number of relay nodes and average degree of nodes are computed. Then the procedure is repeated for k=3. The cost per node defined as the ratio of number of relay nodes to the number of sensor nodes and connectivity improvement defined as a ratio of average degree value provided by resultant minimum k-vertex graph to number of relay nodes placed are shown in fig. 3 and 4 respectively.
Fig. 1. Relay nodes Vs. Sensor nodes for K=2
Fig. 3. Connectivity Improvement Vs. Sensor nodes
Fig. 2. . Relay nodes Vs. Sensor nodes for K=3
Fig. 4. Relay Cost Vs. Sensor nodes
In performances shown in Fig 1, and 2, we observe initially for smaller number of sensor nodes, the relay nodes placed by PSO-MPC algorithm are in greater number than that of Steiner-MPC. Later as number of sensor nodes increases, the relay nodes placed by PSO-MPC algorithm are goes on decreasing sharply as compared to Steiner-MPC algorithm. With the results, we can easily conclude that, for large scale
735
736
Deepak R Dandekar and P.R. Deshmukh / Procedia Technology 4 (2012) 732 – 736
wireless sensor networks, PSO based method provides optimal solutions and better than Steiner based method under the same network parameter setting, no matter k=2 or 3. Results shown in fig 3 indicate that PSO-MPC algorithm is ahead of Steiner-MPC in concern to network connectivity improvement and cost of relays placed for desired connectivity. 5. Conclusion and Future Work In this work we proposed an algorithm for deploying minimum additional relay nodes to provide multi-path connectivity (k-connectivity) in heterogeneous wireless sensor networks. The algorithm uses swarm intelligence in placing the relay nodes optimally. Performance comparison showed that PSO-MPC perform well over Steiner-MPC. Proposed PSO based algorithm is iterative algorithm which uses lower number of relay nodes deployed to attain desired k-connectivity in given wireless sensor network. The PSO-MPC requires high computational time than Steiner-MPC and it increases with increase in swam population. In future, we would like to conduct similar experiments to find the optimal number of heterogeneous relay node to be placed (relay nodes with different transmission capabilities) for desired kconnectivity in heterogeneous wireless sensor networks. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
Mohamed Younis, Kamal Akkaya, Strategies and Techniques for Node Placement in Wireless Sensor Networks: A Survey. Journal of Ad Hoc Networks Elsevier 6(4) 2008. Xiaofeng Han, Xiang Cao, Errol L. Lloyd, and Chien-Chung Shen: Fault-Tolerant Relay Node Placement in Heterogeneous Wireless Sensor Networks. IEEE Transactions On Mobile Computing, 9(5) May 2010. A. Kashyap, S. Khuller, and M. Shayman: Relay Placement for Higher Order Connectivity in Wireless Sensor Networks. INFOCOM 1-12 Apr 2006. E.L. Lloyd and G. Xue: Relay Node Placement in Wireless Sensor Networks. IEEE Trans. Computers 56(1) Jan. 2007. X. Cheng, D. Du, L. Wang, and B. Xu, Relay Sensor Placement in Wireless Sensor Networks. Journal of Wireless Networks 14(3) June 2008 347-355. Bin Hao,Han Tang,Guoliang Xue, Fault-tolerant relay node placement in wireless sensor networks: formulation and approximation. Proc. IEEE, Workshop on High Performance Switching and Routing 2004 246 – 250. Hisham M. Almasaeid and Ahmed E. Kamal, On the Minimum k-Connectivity Repair in Wireless Sensor Networks. IEEE International Conference on Communication 2009 1-5. Quanhong Wang, Kenan Xu, Glen Takahara and Hossam Hassanein, Device Placement for Heterogeneous Wireless Sensor. Networks: Minimum Cost with Lifetime Constraints. IEEE Transactions On Wireless Communications, Vol. 6(7) July 2007. Juhua Pu, Zhang Xiong, Xiaofeng Lu, Fault-tolerant deployment with k-connectivity and partial k-connectivity in sensor. networks. Journal Wireless Communications and Mobile Computing 9(7), July 2009. Misra, S, Seung Don Hong, Guoliang Xue, Jian Tang, Constrained Relay Node Placement in Wireless Sensor Networks: Formulation and Approximations. ACM/IEEE Transaction on Networking, 18(2 ) 2010. Jonathan L. Bredin, Erik D. Demaine, MohammadTaghi Hajiaghayi, Daniela Ru, Deploying Sensor Networks with Guaranteed Capacity and Fault Tolerance. MobiHoc May 25-27 2005. B. Degener, S.P. Fekete, B. Ksempkes and F.M.A.D. Heide, A survey on relay placement with runtime and approximation guarantees. Computer Science-Review 2011 57-68 . Raghavendra V. Kulkarni and Ganesh Kumar Venayagamoorthy, Particle Swarm Optimization in Wireless Sensor Networks: A Brief Survey. IEEE Transaction on Systems, Man, and Cybernetics, Part C: Applications and Reviews 41(2) March 2011. R. C. Eberhart and Y. Shi, “Evolving artificial neural networks, in: Proc.1998 Int. Conf. Neural Networks and Brain, Beijing P.R.C. 1998. J. Hu, J. Song, M. Zhang, and X. Kang: Topology optimization for urban traffic sensor network. Tsinghua Science & Technology 13 Apr 2008. Kennedy, J. and Eberhart, R. C.: Particle swarm optimization in Proc. IEEE international conference on neural networks 1995.