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• W1542719709 abstract "We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [9] showed a 2/5-approximation for the unconstrained problem and also proved that no approximation better than 1/2 is possible in the value oracle model. Constant-factor approximation has been also known for submodular maximization subject to a matroid independence constraint (a factor of 0.309 [33]) and for submodular maximization subject to a matroid base constraint, provided that the fractional base packing number ν is bounded away from 1 (a 1/4-approximation assuming that ν ≥ 2 [33]).In this paper, we propose a new algorithm for submodular maximization which is based on the idea of simulated annealing. We prove that this algorithm achieves improved approximation for two problems: a 0.41-approximation for unconstrained submodular maximization, and a 0.325-approximation for submodular maximization subject to a matroid independence constraint.On the hardness side, we show that in the value oracle model it is impossible to achieve a 0.478-approximation for submodular maximization subject to a matroid independence constraint, or a 0.394-approximation subject to a matroid base constraint in matroids with two disjoint bases. Even for the special case of cardinality constraint, we prove it is impossible to achieve a 0.491-approximation. (Previously it was conceivable that a 1/2-approximation exists for these problems.) It is still an open question whether a 1/2-approximation is possible for unconstrained submodular maximization." @default.
• W1542719709 created "2016-06-24" @default.
• W1542719709 creator A5017101724 @default.
• W1542719709 creator A5023410548 @default.
• W1542719709 date "2011-01-23" @default.
• W1542719709 modified "2023-09-27" @default.
• W1542719709 title "Submodular maximization by simulated annealing" @default.
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• W1542719709 doi "https://doi.org/10.5555/2133036.2133119" @default.
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