Analysis and improvement of the 3-star algorithm for the STP-MSP problem in Wireless Sensor Networks

A Wireless Sensor Network (WSN) uses a larger number of low-power sensor nodes to gather environmental information which is then wirelessly forwarded to a base station. However, sensor nodes have very limited communication ranges. Thus, relay nodes are required to ensure reliable connectivity throughout the WSN. On the other hand, relay nodes are typically more sophisticated and expensive than sensor nodes. Therefore, deployment strategies should seek to minimize the number of required relay nodes, a problem referred to as the Steiner Tree Problem with Minimum Number of Steiner Points (SMT-MSP), which has been shown to be NP-hard. This paper analyzes and improves the 3-star approximation algorithm by reducing the time complexity from O(n3) to O(nlogn) with the identical performance ratio. Experiments are conducted to verify the correctness of the proposed algorithm.

[1]  Ronald L. Graham,et al.  On the History of the Minimum Spanning Tree Problem , 1985, Annals of the History of Computing.

[2]  Hai Liu,et al.  On optimal placement of relay nodes for reliable connectivity in wireless sensor networks , 2006, J. Comb. Optim..

[3]  Errol L. Lloyd,et al.  Relay Node Placement in Wireless Sensor Networks , 2011, IEEE Transactions on Computers.

[4]  Lusheng Wang,et al.  Approximations for Steiner Trees with Minimum Number of Steiner Points , 2000, Theor. Comput. Sci..

[5]  Athanasios V. Vasilakos,et al.  Efficient location-based topology control algorithms for wireless ad hoc and sensor networks , 2016, Wirel. Commun. Mob. Comput..

[6]  Sang Hyuk Son,et al.  ATPC: Adaptive Transmission Power Control for Wireless Sensor Networks , 2016, TOSN.

[7]  Satyajayant Misra,et al.  Fault-Tolerant Relay Node Placement in Wireless Sensor Networks: Problems and Algorithms , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[8]  Ion I. Mandoiu,et al.  A note on the MST heuristic for bounded edge-length Steiner trees with minimum number of Steiner points , 2000, Inf. Process. Lett..

[9]  Lusheng Wang,et al.  Relay sensor placement in wireless sensor networks , 2008, Wirel. Networks.

[10]  Guohui Lin,et al.  Steiner Tree Problem with Minimum Number of Steiner Points and Bounded Edge-Length , 1999, Inf. Process. Lett..

[11]  Eytan Modiano,et al.  Mobile backbone networks --: construction and maintenance , 2006, MobiHoc '06.