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The Line-Constrained Maximum Coverage Facility Location Problem

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Combinatorial Optimization and Applications (COCOA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14461))

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Abstract

We consider the maximum coverage facility location problem in the plane. In this paper, we restrict the facilities to be located on the given line, and propose an \(O(n^2)\) algorithm for this problem by transforming the problem to the maximum weight k-link path problem in a complete directed acyclic graph, and by proving the concave Monge property inherent to the edge weights of the graph by which the substantial improvement of the running time compared with the straightforward implementation is attained.

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Notes

  1. 1.

    In papers [7, 8], the term convex Monge property is already used without formal definition. However, its definition is obvious from the context, and thus we used this term.

References

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers 19H04068, 23H03349. The research conducted in this paper was motivated by our collaborative research with XYMAX Corporation and XYMAX REAL ESTATE INSTITUTE Corporation [4]. We also gratefully acknowledge the financial support from these two companies.

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Authors and Affiliations

  1. University of Hyogo, Kobe, Japan

    Hiroki Maegawa, Naoki Katoh, Yuki Tokuni & Yuya Higashikawa

Authors
  1. Hiroki Maegawa
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  2. Naoki Katoh
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  3. Yuki Tokuni
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  4. Yuya Higashikawa
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Corresponding author

Correspondence to Hiroki Maegawa .

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Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Beijing Normal University, Zhuhai, China

    Jianxiong Guo

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Maegawa, H., Katoh, N., Tokuni, Y., Higashikawa, Y. (2024). The Line-Constrained Maximum Coverage Facility Location Problem. In: Wu, W., Guo, J. (eds) Combinatorial Optimization and Applications. COCOA 2023. Lecture Notes in Computer Science, vol 14461. Springer, Cham. https://doi.org/10.1007/978-3-031-49611-0_29

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  • DOI: https://doi.org/10.1007/978-3-031-49611-0_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49610-3

  • Online ISBN: 978-3-031-49611-0

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