Efficient emulation of single-hop radio network with collision detection on multi-hop radio network with no collision detection

Abstract

This paper presents an efficient randomized emulation of single-hop radio network with collision detection on multi-hop radio network without collision detection. Each step of the single-hop network is emulated by O((D+logn/ε)logΔ) rounds of the multi-hop network and succeeds with probability ≥1−ɛ. (n is the number of processors, D the diameter and Δ the maximum degree). It is shown how to emulate any polynomial algorithm such the probability of failure remains ≤ɛ. A consequence of the emulation is an efficient randomized algorithm for choosing a leader in a multi-hop network.