Leader election in SINR model with arbitrary power control

Abstract

We consider the Leader Election Problem in the Signal-to-Interference-plusNoise-Ratio (SINR) model where nodes can adjust their transmission power. We show that in this setting it is possible to elect a leader in two communication rounds, with high probability. Previously, it was known that Θ(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 every 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 complement this with an algorithm that uses power range 2O˜(n)1, when n is known, and 2O˜(n 1.5 ) , 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 range of possible power levels of size exp(n 1/Θ(t) ) is sufficient and necessary