Abstract

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology control algorithm. This algorithm does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node u transmits with the minimum power p u,# required to ensure that in every cone of degree # around u, there is some node that u can reach with power p u,# . We show that taking # = 5#/6 is a necessary and su#cient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from s to t when every node communicates at maximum power then, if # 5#/6, there is still a path in the smallest symmetric graph G # containing all edges (u, v) such that u can communicate with v using power p u,# . On the other hand, if # > 5#/6, # This is a revised and extended version of "Analysis of a cone-based topology control algorithm for wireless multi-hop networks", which appeared in Proceedings of ACM Principles of Distributed Computing (PODC), 2001, and includes results from "Distributed topology control for power e#cient operation in multihop wireless ad hoc networks", by R. Wattenhofer, L. Li, P. Bahl, and Y. M. Wang, which appeared in Proceedings of IEEE INFOCOM, 2001.

Citations