Space Bounds for Adaptive Renaming
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by
Maryam Helmi, Lisa Higham, Philipp Woelfel
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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