Constrained Submodular Maximization via a Nonsymmetric Technique

The study of combinatorial optimization problems with submodular objectives has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining further improvements for many submodular maximization proble...

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Published inMathematics of operations research Vol. 44; no. 3; pp. 988 - 1005
Main Authors Buchbinder, Niv, Feldman, Moran
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.08.2019
Institute for Operations Research and the Management Sciences
Subjects
Algorithms
approximation algorithm
Combinatorial analysis
Constraints
Expectation-maximization algorithm
Mathematical optimization
Mathematical research
Maximization
multilinear relaxation
Operations research
Optimization
Profit maximization
Relaxation methods (Mathematics)
Studies
submodular maximization
Israel
Online AccessGet full text
ISSN0364-765X
1526-5471
DOI10.1287/moor.2018.0955

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Abstract The study of combinatorial optimization problems with submodular objectives has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining further improvements for many submodular maximization problems boils down to finding better algorithms for optimizing a relaxation of them known as the multilinear extension. In this work, we present an algorithm for optimizing the multilinear relaxation whose guarantee improves over the guarantee of the best previous algorithm (by Ene and Nguyen). Moreover, our algorithm is based on a new technique that is, arguably, simpler and more natural for the problem at hand. In a nutshell, previous algorithms for this problem rely on symmetry properties that are natural only in the absence of a constraint. Our technique avoids the need to resort to such properties, and thus seems to be a better fit for constrained problems.
AbstractList The study of combinatorial optimization problems with submodular objectives has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining further improvements for many submodular maximization problems boils down to finding better algorithms for optimizing a relaxation of them known as the multilinear extension. In this work, we present an algorithm for optimizing the multilinear relaxation whose guarantee improves over the guarantee of the best previous algorithm (by Ene and Nguyen). Moreover, our algorithm is based on a new technique that is, arguably, simpler and more natural for the problem at hand. In a nutshell, previous algorithms for this problem rely on symmetry properties that are natural only in the absence of a constraint. Our technique avoids the need to resort to such properties, and thus seems to be a better fit for constrained problems.
Audience Academic
Author Buchbinder, Niv
Feldman, Moran
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Snippet The study of combinatorial optimization problems with submodular objectives has attracted much attention in recent years. Such problems are important in both...
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SubjectTerms Algorithms
approximation algorithm
Combinatorial analysis
Constraints
Expectation-maximization algorithm
Mathematical optimization
Mathematical research
Maximization
multilinear relaxation
Operations research
Optimization
Profit maximization
Relaxation methods (Mathematics)
Studies
submodular maximization
Title Constrained Submodular Maximization via a Nonsymmetric Technique
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