文章基本信息

标题：The Cover Number of a Matrix and its Algorithmic Applications
本地全文：下载
作者：Noga Alon ; Troy Lee ; Adi Shraibman 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2014
卷号：28
页码：34-47
DOI：10.4230/LIPIcs.APPROX-RANDOM.2014.34
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Given a matrix A, we study how many epsilon-cubes are required to cover the convex hull of the columns of A. We show bounds on this cover number in terms of VC dimension and the gamma_2 norm and give algorithms for enumerating elements of a cover. This leads to algorithms for computing approximate Nash equilibria that unify and extend several previous results in the literature. Moreover, our approximation algorithms can be applied quite generally to a family of quadratic optimization problems that also includes finding the k-by-k combinatorial rectangle of a matrix. In particular, for this problem we give the first quasi-polynomial time additive approximation algorithm that works for any matrix A in [0,1]^{m x n}.
关键词：Approximation algorithms; Approximate Nash equilibria; Cover number; VC dimension