Greedy Maximization of Functions with Bounded Curvature under Partition Matroid Constraints
| Autor: | Frank Neumann, Francesco Quinzan, Ralf Rothenberger, Andreas Göbel, Tobias Friedrich |
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| Rok vydání: | 2018 |
| Předmět: |
TheoryofComputation_MISCELLANEOUS
FOS: Computer and information sciences Mathematical optimization Computer Science::Computer Science and Game Theory Discrete Mathematics (cs.DM) Heuristic Computer science Maximum cut TheoryofComputation_GENERAL Monotonic function General Medicine Directed graph Maximization Positive-definite matrix Matroid Submodular set function Monotone polygon Subadditivity Greedy algorithm Computer Science - Discrete Mathematics |
| Zdroj: | AAAI |
| DOI: | 10.48550/arxiv.1811.05351 |
| Popis: | We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though constrained maximization problems of monotone submodular functions have been extensively studied, little is known about greedy maximization of non-monotone submodular functions or monotone subadditive functions. We give approximation guarantees for GREEDY on these problems, in terms of the curvature. We find that this simple heuristic yields a strong approximation guarantee on a broad class of functions. We discuss the applicability of our results to three real-world problems: Maximizing the determinant function of a positive semidefinite matrix, and related problems such as the maximum entropy sampling problem, the constrained maximum cut problem on directed graphs, and combinatorial auction games. We conclude that GREEDY is well-suited to approach these problems. Overall, we present evidence to support the idea that, when dealing with constrained maximization problems with bounded curvature, one needs not search for approximate) monotonicity to get good approximate solutions. Comment: 12 pages, 5 figures, Conference version at the the 33rd AAAI Conference on Artificial Intelligence (AAAI'19), code of algorithms and experiments available at http://github.com/RalfRothenberger/Greedy-Maximization-of-Functions-with-Bounded-Curvature-under-Partition-Matroid-Constraints |
| Databáze: | OpenAIRE |
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