Space Bounds for Adaptive Renaming release_ke6jugrssfesbdfonypjouwssa

by Maryam Helmi, Lisa Higham, Philipp Woelfel

Released as a article .

2016  

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. As a result of an f-adaptive renaming algorithm each participating process gets a distinct name in the range {1,...,f(k)} provided k processes participate. Let f: {1,...,n}→N be a non-decreasing function satisfying f(1) ≤ n-1 and let d = {x | f(x) ≤ n-1}. We show that any non-deterministic solo-terminating long-lived f-adaptive renaming object requires d + 1 registers. This implies a lower bound of n-c registers for long-lived (k+c)-adaptive renaming, which we observe is tight. We also prove a lower bound of 2(n - c)/c+2 registers for implementing any non-deterministic solo-terminating one-shot (k+c)-adaptive renaming. We provide two one-shot renaming algorithms: a wait-free algorithm and an obstruction-free algorithm. Each algorithm employs a parameter to depict the tradeoff between space and adaptivity. When these parameters are chosen appropriately, this results in a wait-free one-shot (3k^2/2)-adaptive renaming algorithm from √(n) + 1 registers, and an obstruction-free one-shot f-adaptive renaming algorithm from only {n, x | f(x) ≥ 2n} + 1 registers.
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Date   2016-03-19
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arXiv  1603.04067v3
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