Affiliation:
1. University of Liverpool, Liverpool, UK
2. University of Connecticut, Storrs, CT
Abstract
The problem of performing
n
tasks on
p
asynchronous or undependable processors is a basic problem in distributed computing. This article considers an abstraction of this problem called
Write-All: using p processors write 1's into all locations of an array of size n
. In this problem writing 1 abstracts the notion of performing a simple task. Despite substantial research, there is a dearth of efficient deterministic asynchronous algorithms for
Write-All/
. Efficiency of algorithms is measured in terms of
work
that accounts for all local steps performed by the processors in solving the problem. Thus, an optimal algorithm would have work Θ(
n
), however it is known that optimality cannot be achieved when
p
= Ω(
n
). The quest then is to obtain work-optimal solutions for this problem using a nontrivial, compared to
n
, number of processors
p
. The algorithm presented in this article has work complexity of
O
(
n
+
p
2 + ϵ
), and it achieves work optimality for
p
=
O
(
n
1/(2 + ε)
) for any ε > 0, while the previous best result achieved optimality for
p
≤4√
n
/log
n
. Additionally, the new result uses
only
the atomic read/write memory, without resorting to using the test-and-set primitive that was necessary in the previous solution.
Funder
National Science Foundation
North Atlantic Treaty Organization
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
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