Contention resolution with log-logstar channel accesses

For decades, randomized exponential backoff has provided a critical algorithmic building block in situations where multiple devices seek access to a shared resource. Surprisingly, despite this history, the performance of standard backoff is poor under worst-case scheduling of demands on the resource: (i) subconstant throughput can occur under plausible scenarios, and (ii) each of N devices requires Omega(log N) access attempts before obtaining the resource. In this paper, we address these shortcomings by offering a new backoff protocol for a shared communications channel that guarantees expected constant throughput with only O(log(log* N)) access attempts in expectation. Central to this result are new algorithms for approximate counting and leader election with the same performance guarantees.