Improved Approximation Algorithms for Label Cover Problems

Moses Charikar, MohammadTaghi Hajiaghayi, Howard J. Karloff

Abstract: In this paper we consider both the maximization variant Max Rep and the minimization variant Min Rep of the famous Label Cover problem, for which, till now, the best approximation ratios known were $O(\sqrt n)$ . In fact, several recent papers reduced Label Cover to other problems, arguing that if better approximation algorithms for their problems existed, then a $o(\sqrt n)$ -approximation algorithm for Label Cover would exist. We show, in fact, that there are a O(n 1/3)-approximation algorithm for Max Rep and a O(n 1/3log2/3 n)-approximation algorithm for Min Rep. In addition, we also exhibit a randomized reduction from Densest k -Subgraph to Max Rep, showing that any approximation factor for Max Rep implies the same factor (up to a constant) for Densest k -Subgraph.