A sublinear-time randomized approximation algorithm for matrix games

This paper presents a parallel randomized algorithm which computes a pair of ε-optimal strategies for a given ( m, n)-matrix game A = [ a ij ] ϵ [−1, 1] in O( ε −2log 2( n+ m)) expected time on an ( n+ m)/log( n+ m)-processor EREW PRAM. For any fixed accuracy ϵ > 0, the expected sequential runnin...

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Bibliographic Details
Published in:Operations research letters Vol. 18; no. 2; pp. 53 - 58
Main Authors: Grigoriadis, Michael D., Khachiyan, Leonid G.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.1995
Elsevier
Subjects:
Applied sciences
Approximation algorithms
Complexity
Exact sciences and technology
Game theory
Linear programming
Matrix games
Operational research and scientific management
Operational research. Management science
Parallel algorithms
Randomized algorithms
Matrix games
Approximation algorithms
Linear programming
Randomized algorithms
Parallel algorithms
Complexity
Lower bound
Algorithms
Approximation
Deterministic approach
Computational complexity
Matrix game
Game theory
ISSN:0167-6377, 1872-7468
Online Access:Get full text
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Summary:This paper presents a parallel randomized algorithm which computes a pair of ε-optimal strategies for a given ( m, n)-matrix game A = [ a ij ] ϵ [−1, 1] in O( ε −2log 2( n+ m)) expected time on an ( n+ m)/log( n+ m)-processor EREW PRAM. For any fixed accuracy ϵ > 0, the expected sequential running time of the suggested algorithm is O(( n + m)log( n + m)), which is sublinear in mn, the number of input elements of A. On the other hand, simple arguments are given to show that for ε < 1 2 , any deterministic algorithm for computing a pair of ε-optimal strategies of an ( m, n)-matrix game A with ± 1 elements examines Ω(mn) of its elements. In particular, for m = n the randomized algorithm achieves an almost quadratic expected speedup relative to any deterministic method.
ISSN:0167-6377
1872-7468
DOI:10.1016/0167-6377(95)00032-0