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.
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References
Austrin, P.: Improved Inapproximability For Submodular Maximization. arXiv:1004.3777v1 [cs.CC] (2010)
Austrin, P., Mossel, E.: Approximation Resistant Predicates from Pairwise Independence. Computational Complexity 18(2), 249–271 (2009)
Feige, U., Mirrokni, V.S., Vondrák, J.: Maximizing non-monotone submodular functions. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 461–471 (2007)
Goemans, M.X., Williamson, D.P.: Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming. Journal of the ACM 42, 1115–1145 (1995)
Grötschel, M., Lovász, L., Schrijver, A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2), 169–197 (1981)
Khot, S.: On the Power of Unique 2-prover 1-round Games. In: ACM Symposium on Theory of Computing (STOC), pp. 767–775 (2002)
Lovász, L.: Submodular functions and convexity. In: Grötschel, M., Bachem, A., Korte, B. (eds.) Mathematical Programming: The State of the Art - Bonn 1982, pp. 235–257. Springer, Heidelberg (1983)
Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions–I. Mathematical Programming 14, 265–294 (1978)
Vondrák, J.: Submodular maximization by simulated annealing. Unpublished manuscript
Vondrák, J.: Submodularity in Combinatorial Optimization. PhD thesis, Charles University (2007)
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Austrin, P. (2010). Improved Inapproximability for Submodular Maximization. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2010 2010. Lecture Notes in Computer Science, vol 6302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15369-3_2
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DOI: https://doi.org/10.1007/978-3-642-15369-3_2
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