Space Bounds for Adaptive Renaming

Abstract

We study the space complexity of implementing long-lived and one-shot 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 $\lfloor \frac{n}{c+1} \rfloor$ 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 $(\frac{3k^2}{2})$-adaptive one from $\lceil \sqrt{n} \rceil$ registers, and an obstruction-free one-shot f(k)-adaptive renaming algorithm from only ⌈f ^− 1(n) ⌉ registers.

This research was undertaken, in part, thanks to funding from the Canada Research Chairs program, the Discovery Grants program of the Natural Sciences and Engineering Research Council of Canada (NSERC), and Alberta Innovates Technology Futures (AITF).