2014
DOI: 10.1137/110839655
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Submodular Function Maximization via the Multilinear Relaxation and Contention Resolution Schemes

Abstract: We consider the problem of maximizing a non-negative submodular set function f : 2 N → R+ over a ground set N subject to a variety of packing type constraints including (multiple) matroid constraints, knapsack constraints, and their intersections. In this paper we develop a general framework that allows us to derive a number of new results, in particular when f may be a non-monotone function. Our algorithms are based on (approximately) solving the multilinear extension F of f [5] over a polytope P that represe… Show more

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Cited by 224 publications
(431 citation statements)
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References 49 publications
(148 reference statements)
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“…Given the previous result on cardinality constraints, several extensions have been considered, such as knapsack constraints or matroid constraints (see [42] and references therein). Moreover, fast algorithms and improved online data-dependent bounds can be further derived [150].…”
Section: Maximization With Cardinality Constraintsmentioning
confidence: 99%
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“…Given the previous result on cardinality constraints, several extensions have been considered, such as knapsack constraints or matroid constraints (see [42] and references therein). Moreover, fast algorithms and improved online data-dependent bounds can be further derived [150].…”
Section: Maximization With Cardinality Constraintsmentioning
confidence: 99%
“…When the function is known to be non-negative (i.e., with non-negative values F (A) for all A ⊆ V ), then simple local search algorithm have led to theoretical guarantees [67,42,33]. It has first been shown in [67] that a 1/2 relative bound could not be improved in general if a polynomial number of queries of the submodular function is used.…”
Section: Proof Ifmentioning
confidence: 99%
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“…In this section, we extend our results to submodular objectives by combining the results from the previous section with the framework from [15]. Let N be a finite ground set.…”
Section: Submodular Objective Via the Cr Scheme Frameworkmentioning
confidence: 84%
“…The problem of maximizing submodular functions subject to various constraints is very well-studied; we refer the reader to [15] for an overview. UFP with a linear objective is also extensively studied.…”
Section: Theoremmentioning
confidence: 99%