Space Bounds for Adaptive Renaming

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 = max{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 soloterminating one-shot (k+ c)-adaptive renaming. We provide two one-shot renaming algorithms: a waitfree 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 min{n,x | f (x)≥ 2n}+1 registers. [email protected], +1 403 210-9416 [email protected], +1 403 220-7696 [email protected], +1 403 220-7259