Brief Announcement: Leader Election in SINR Model with Arbitrary Power Control

In this article, we study the leader election problem in the Signal-to-Interference-plus-Noise-Ratio (SINR) model where nodes can adjust their transmission power. We show that in this setting it is possible to solve the leader election problem in two communication rounds, 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 then examine how much power control is needed to achieve fast leader election. We show that any 2-round leader election algorithm in the SINR model running correctly w.h.p. requires a power range 2Ω(n) even when n is known. We match this with an algorithm that uses power range 2θ(n), when n is known and 2Õ(n1.5) when n is not known. We also explore tradeoffs between time and power used, and show that to elect a leader in t rounds, a power range exp(n1θ(t)) is sufficient and necessary.