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The Cover Number of a Matrix and its Algorithmic Applications Alon, Noga Lee, Troy Shraibman, Adi Approximation algorithms Approximate Nash equilibria Cover number VC dimension 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}. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Noga Alon and Troy Lee and Adi Shraibman 2014 Is Part Of LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX-RANDOM.2014.34 urn:nbn:de:0030-drops-46865 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.34 eng https://creativecommons.org/licenses/by/3.0/legalcode