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DOI: 10.4230/LIPIcs.ESA.2024.102

SubModST: A Fast Generic Solver for Submodular Maximization with Size Constraints

Authors: Henning Martin Woydt, Christian Komusiewicz, and Frank Sommer

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract

In the Cardinality-Constrained Maximization (Minimization) problem the input is a universe 𝒰, a function f: 2^{{𝒰}} → ℝ, and an integer k, and the task is to find a set S ⊆ 𝒰 with |S| ≤ k that maximizes (minimizes) f(S). Many well-studied problems such as Facility Location, Partial Dominating Set, Group Closeness Centrality and Euclidean k-Medoid Clustering are special cases of Cardinality-Constrained Maximization (Minimization). All the above-mentioned problems have the diminishing return property, that is, the improvement of adding an element e ∈ 𝒰 to a set S is at least as large as adding e to any superset of S. This property is called submodularity for maximization problems and supermodularity for minimization problems. In this work we develop a new exact branch-and-cut algorithm SubModST for the generic Submodular Cardinality-Constrained Maximization and Supermodular Cardinality-Constrained Minimization. We develop several speed-ups for SubModST and we show their effectiveness on six example problems. We show that SubModST outperforms the state-of-the-art solvers developed by Csókás and Vinkó [J. Glob. Optim. '24] and Uematsu et al. [J. Oper. Res. Soc. Japan '20] for Submodular Cardinality-Constrained Maximization by orders of magnitudes.

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Henning Martin Woydt, Christian Komusiewicz, and Frank Sommer. SubModST: A Fast Generic Solver for Submodular Maximization with Size Constraints. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 102:1-102:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{woydt_et_al:LIPIcs.ESA.2024.102,
  author =	{Woydt, Henning Martin and Komusiewicz, Christian and Sommer, Frank},
  title =	{{SubModST: A Fast Generic Solver for Submodular Maximization with Size Constraints}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{102:1--102:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.102},
  URN =		{urn:nbn:de:0030-drops-211730},
  doi =		{10.4230/LIPIcs.ESA.2024.102},
  annote =	{Keywords: Branch-and-Cut, Lazy Evaluations, Facility Location, Group Closeness Centrality, Partial Dominating Set}
}

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SubModST: A Fast Generic Solver for Submodular Maximization with Size Constraints

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