The Cover Number of a Matrix and its Algorithmic Applications

Noga Alon, Troy Lee, Adi Shraibman, Marc Herbstritt
2014 International Workshop on Approximation Algorithms for Combinatorial Optimization  
Given a matrix A, we study how many -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 γ 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
more » ... ludes finding the densest 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 ∈ [0, 1] m×n .
doi:10.4230/lipics.approx-random.2014.34 dblp:conf/approx/AlonLS14 fatcat:nzvswv4g25ambl3skaj5c5gafi