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

Authors Henning Martin Woydt , Christian Komusiewicz , Frank Sommer

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Branch-and-bound
Keywords
  • Branch-and-Cut
  • Lazy Evaluations
  • Facility Location
  • Group Closeness Centrality
  • Partial Dominating Set

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ESA.2024.102

Author Details

Henning Martin Woydt
  • Heidelberg University, Germany
Christian Komusiewicz
  • Friedrich Schiller University Jena, Institute of Computer Science, Germany
Frank Sommer
  • Friedrich Schiller University Jena, Institute of Computer Science, Germany

Funding

  • Woydt, Henning Martin: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - DFG SCHU 2567/6-1.

Acknowledgements

The results of this work are based on the first author’s Masters thesis [Henning M. Woydt, 2023].

Supplementary Materials

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