The loudest one wins : efficient communication in theoretical wireless networks

Abstract

In order to develop the most efficient algorithms for wireless networks, first one must understand their theoretical limitations. To this end, we study the leader election and broadcast problems in wireless networks, modeling them using the Signal-to- Interference-plus-Noise-Ratio (SINR) model. Our main result is an algorithm that solves the leader election problem in two communication rounds using power control, with high probability. Previously, it was known that [Omega](log n) rounds were sufficient and necessary when using uniform power, where n is the number of nodes in the network. We explore tradeoffs between communication complexity and power used, and show that to elect a leader in t rounds, a power range exp (n (1 [Theta] T) is sufficient and necessary. In addition, we present an efficient algorithm for the broadcast problem. Using power control, it is possible to achieve a broadcast algorithm that terminates successfully in 2n rounds, w.h.p..