Relay Nodes in Wireless Sensor Networks

• Authors: Gruia Călinescu;Sutep Tongngam
• Venue: WASA '08 Proceedings of the Third International Conference on Wireless Algorithms, Systems, and Applications
• Year: 2008

Motivated by application to wireless sensor networks, we study the following problem. We are given a set Sof wireless sensor nodes, given as a set of points in the two-dimensional plane, and real numbers 0 r≤ R. We must place a minimum-size set Qof wireless relay nodes in the two dimensional plane to connect S, where connectivity is explained formally next. The nodes of Scan communicate to nodes within distance r, and the relay nodes of Qcan communicate within distance R. Once the nodes of Qare placed, they together with Sinducean undirected graph G= (V,E) defined as follows: V= S驴 Q, and $E = \{ uv | u,v \in Q \mbox{ and } ||u,v|| \leq R \} \cup \{ xu | x \in S \mbox{ and } u \in (Q \cup S) \mbox{ and } ||u,x|| \leq r\}$, where ||u,v|| denotes the Euclidean distance from uto v. Gmust be connected.It was shown in [1] that an algorithm based on Minimum Spanning Tree achieves approximation ratio 7. We improve the analysis of this algorithm to 6, and propose a post-processing heuristic called Post-Order Greedyto practically improve the performance of the approximation algorithms. Experiments on random instances give Post-Order Greedy applied after Minimum Spanning Tree an average improvement of up to 23%. Applying Post-Order Greedy after an optimum Steiner Tree algorithm results in another circa 6% improvement considering the same instances.