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The Constrained 2-Maxian Problem on Cycles

Author

Listed:
  • Chunsong Bai

    (School of Finance and Mathematics, Huainan Normal University, Huainan 232038, China)

  • Jun Du

    (School of Finance and Mathematics, Huainan Normal University, Huainan 232038, China)

Abstract

This paper deals with p -maxian problem on cycles with an upper bound on the distances of all facilities. We consider the case of p = 2 and show that, in the worst case, the optimal solution contains at least one vertex of the underlying cycle, which helps to develop an efficient algorithm to solve the constrained 2-maxian problem. Based on this property, we develop a linear time algorithm for the constrained 2-maxian problem on a cycle. We also discuss the relations between the constrained and unconstrained 2-maxian problems on which the underlying graphs are cycles.

Suggested Citation

  • Chunsong Bai & Jun Du, 2024. "The Constrained 2-Maxian Problem on Cycles," Mathematics, MDPI, vol. 12(6), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:876-:d:1358266
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    References listed on IDEAS

    as
    1. G. Y. Handler, 1973. "Minimax Location of a Facility in an Undirected Tree Graph," Transportation Science, INFORMS, vol. 7(3), pages 287-293, August.
    2. A. J. Goldman, 1971. "Optimal Center Location in Simple Networks," Transportation Science, INFORMS, vol. 5(2), pages 212-221, May.
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