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A sublinear-time randomized approximation algorithm for matrix games

Author: Michael D Grigoriadis; Leonid Khachiyan
Publisher: New Brunswick, N.J. : Rutgers University, Dept. of Computer Science, Laboratory for Computer Science Research, [1994]
Series: Rutgers University.; Department of Computer Science.; Laboratory for Computer Science Research.; Technical report
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
Abstract: "This paper presents a parallel randomized algorithm which computes a pair of [epsilon]-optimal strategies for a given (m, n)- matrix game A = [a[subscript i, subscript j]] [is in the set of] [-1,1] in O([epsilon][superscript-2] log² (n + m)) expected time on an (n + m) / log (n + m)-processor EREW PRAM. This algorithm is a natural extension of the classical method of fictitious play by Brown and Robinson.  Read more...
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Document Type: Book
All Authors / Contributors: Michael D Grigoriadis; Leonid Khachiyan
OCLC Number: 33248849
Notes: "April 15, 1994."
Description: 8 pages ; 28 cm.
Series Title: Rutgers University.; Department of Computer Science.; Laboratory for Computer Science Research.; Technical report
Responsibility: M.D. Grigoriadis and L.G. Khachiyan.

Abstract:

Abstract: "This paper presents a parallel randomized algorithm which computes a pair of [epsilon]-optimal strategies for a given (m, n)- matrix game A = [a[subscript i, subscript j]] [is in the set of] [-1,1] in O([epsilon][superscript-2] log² (n + m)) expected time on an (n + m) / log (n + m)-processor EREW PRAM. This algorithm is a natural extension of the classical method of fictitious play by Brown and Robinson. For any fixed accuracy [epsilon]> 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 [epsilon] <1/2, any sequential deterministic algorithm for computing a pair of [epsilon]-optimal strategies of an (m, n)- matrix game A with [plus or minus] 1 elements examines [omega] (m, n) of its elements. In particular, for m = n the randomized algorithm achieves an almost quadratic expected speedup relative to any deterministic method."

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