Contention Resolution on Multiple Channels with Collision Detection

In this paper, we consider the classical contention resolution problem in which an unknown subset of n possible nodes are activated and connected to a shared channel. The problem is solved in the first round that an active node transmits alone (thus breaking symmetry). Contention resolution has been an active research topic for over four decades. Accordingly, tight upper and lower bounds are known for most major model assumptions. There remains, however, an important case that is unresolved: contention resolution with multiple channels and collision detection. (Tight bounds are known for contention resolution with multiple channels, and contention resolution with collision detection, but not for the combination of both assumptions.) Recent work [14] proved the first non-trivial lower bound for randomized solutions to this problem in this setting. The optimality of this lower bound was left an open question. In this paper, we answer this open question by describing and analyzing new contention resolution algorithms that match, or come within a log log log n factor of matching, this bound for all relevant parameters. By doing so, we help advance our understanding of an important longstanding problem. Of equal importance, our solutions introduce a novel new technique in which we leverage a distributed structure we call coalescing cohorts to simulate a well-known parallel search strategy from the structured PRAM CREW model [16] in our unstructured distributed model. We conjecture that this approach is relevant to many problems in the increasingly important setting of distributed computation using multiple shared channels.