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Maximizing Non-Monotone Submodular Functions under Matroid and Knapsack Constraints

By Jon Lee, Vahab S. Mirrokni, Viswanath Nagarajan and Maxim Sviridenko


Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum entropy sampling, and maximum facility location problems. Unlike submodular minimization, submodular maximization is NP-hard. In this paper, we give the first constant-factor approximation algorithm for maximizing any non-negative submodular function subject to multiple matroid or knapsack constraints. We emphasize that our results are for non-monotone submodular functions. In particular, for any constant k, we present

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Year: 2007
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