New performance guarantees for the greedy maximization of submodular set functions

We present new tight performance guarantees for the greedy maximization of monotone submodular set functions. Our main result first provides a performance guarantee in terms of the overlap of the optimal and greedy solutions. As a consequence we improve performance guarantees of Nemhauser et al. (Ma...

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Bibliographic Details
Published inOptimization letters Vol. 11; no. 4; pp. 655 - 665
Main Authors Laitila, Jussi, Moilanen, Atte
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2017
Subjects
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Greedy algorithm
Steepest ascent
Approximation
Maximization
Cardinality
Convex optimization
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Summary:We present new tight performance guarantees for the greedy maximization of monotone submodular set functions. Our main result first provides a performance guarantee in terms of the overlap of the optimal and greedy solutions. As a consequence we improve performance guarantees of Nemhauser et al. (Math Program 14:265–294, 1978 ) and Conforti and Cornuéjols (Discr Appl Math 7:251–274, 1984 ) for maximization over subsets, which are at least half the size of the problem domain. As a further application, we obtain a new tight approximation guarantee in terms of the cardinality of the problem domain.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-016-1039-z