Space bounds for adaptive renaming

Abstract

We study the space complexity of implementing long-lived and oneshot adaptive renaming from multi-reader multi-writer registers, in an asynchronous distributed system with n processes. In an f (k)-adaptive renaming algorithm each participating process gets a distinct name, in the range {1, …, f (k)} provided k processes participate. We show that any obstruction-free long-lived f (k)-adaptive renaming object requires m registers, where m ≤ n−1 is the largest integer such that f (m) ≤ n−1. This implies a lower bound of n−c registers for long-lived (k+c)-adaptive renaming, which is tight. We also prove a lower bound of registers for implementing any obstruction-free one-shot (k+c)-adaptive renaming. We also provide one-shot renaming algorithms, e.g., a wait-free one-shot -adaptive one from registers, and an obstruction-free one-shot f (k)- adaptive renaming algorithm from only registers.