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
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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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