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Improved Approximation Algorithms for Label Cover Problems

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Abstract

In this paper we consider both the maximization variant Max Rep and the minimization variant Min Rep of the famous Label Cover problem. So far the best approximation ratios known for these two problems were \(O(\sqrt{n})\) and indeed some authors suggested the possibility that this ratio is the best approximation factor for these two problems. We show, in fact, that there are a O(n 1/3)-approximation algorithm for Max Rep and a O(n 1/3log 2/3 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.

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Authors and Affiliations

  1. Department of Computer Science, Princeton University, Princeton, NJ, 08540, USA

    Moses Charikar

  2. University of Maryland at College Park, A.V. Williams Bldg., College Park, MD, 20742, USA

    MohammadTaghi Hajiaghayi

  3. AT&T Labs—Research, 180 Park Ave., Florham Park, NJ, 07932, USA

    MohammadTaghi Hajiaghayi & Howard Karloff

Authors
  1. Moses Charikar
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  2. MohammadTaghi Hajiaghayi
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  3. Howard Karloff
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Correspondence to Moses Charikar.

Additional information

A preliminary version of this paper appeared in the 17th Annual European Symposium on Algorithms (ESA ’09).

M. Charikar was supported by NSF ITR grant CCF-0426582, NSF CAREER award CCF-0237113, MSPA-MCS award 0528414, and NSF expeditions award 0832797.

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Charikar, M., Hajiaghayi, M. & Karloff, H. Improved Approximation Algorithms for Label Cover Problems. Algorithmica 61, 190–206 (2011). https://doi.org/10.1007/s00453-010-9464-3

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