Improved inapproximability for submodular maximization

Authors:
Per Austrin
Affiliations:
Courant Institute of Mathematical Sciences, New York University
Venue:
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Year:
2010

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Abstract

We show that it is Unique Games-hard to approximate the maximum of a submodular function to within a factor 0.695, and that it is Unique Games-hard to approximate the maximum of a symmetric submodular function to within a factor 0.739. These results slightly improve previous results by Feige, Mirrokni and Vondrák (FOCS 2007) who showed that these problems are NP-hard to approximate to within 3/4 + ε ≅ 0.750 and 5/6 + ε ≅ 0.833, respectively.