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Type: Conference paper
Title: Greedy maximization of functions with bounded curvature under partition matroid constraints
Author: Friedrich, T.
Goebel, A.
Neumann, F.
Quinzan, F.
Rothenberger, R.
Citation: Proceedings of the ... AAAI Conference on Artificial Intelligence. AAAI Conference on Artificial Intelligence, 2019, vol.33, iss.1, pp.2272-2279
Publisher: Association for the Advancement of Artificial Intelligence
Publisher Place: Palo Alto, CA
Issue Date: 2019
Series/Report no.: AAAI Conference on Artificial Intelligence
ISBN: 9781577358091
ISSN: 2159-5399
Conference Name: AAAI Conference on Artificial Intelligence (AAAI) (27 Jan 2019 - 1 Feb 2019 : Honolulu, HI)
Statement of
Tobias Friedrich, Andreas Göbel, Frank Neumann, Francesco Quinzan, Ralf Rothenberger
Abstract: 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.
Description: AAAI-19/IAAI-19/EAAI-19 Proceedings: Thirty-Third AAAI Conference on Artificial Intelligence Thirty-First Conference on Innovative Applications of Artificial Intelligence The Ninth Symposium on Educational Advances in Artificial Intelligence
Rights: Copyright c 2019, Association for the Advancement of Artificial Intelligence ( All rights reserved.
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