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The maximum ratio clique problem

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  • Samyukta Sethuraman
  • Sergiy Butenko

Abstract

This paper introduces a fractional version of the classical maximum weight clique problem, the maximum ratio clique problem, which is to find a maximal clique that has the largest ratio of benefit and cost weights associated with the clique’s vertices. NP-completeness of the decision version of the problem is established, and three solution methods are proposed. The results of numerical experiments with standard graph instances, as well as with real-life instances arising in finance and energy systems, are reported. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Samyukta Sethuraman & Sergiy Butenko, 2015. "The maximum ratio clique problem," Computational Management Science, Springer, vol. 12(1), pages 197-218, January.
    • Handle: RePEc:spr:comgts:v:12:y:2015:i:1:p:197-218
    DOI: 10.1007/s10287-013-0197-z
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    References listed on IDEAS

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    1. Wu, Tai-Hsi, 1997. "A note on a global approach for general 0-1 fractional programming," European Journal of Operational Research, Elsevier, vol. 101(1), pages 220-223, August.
    2. Oleksii Ursulenko & Sergiy Butenko & Oleg Prokopyev, 2013. "A global optimization algorithm for solving the minimum multiple ratio spanning tree problem," Journal of Global Optimization, Springer, vol. 56(3), pages 1029-1043, July.
    3. Nimrod Megiddo, 1979. "Combinatorial Optimization with Rational Objective Functions," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 414-424, November.
    4. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Cited by:

    1. Shaoning Han & Andrés Gómez & Oleg A. Prokopyev, 2022. "Fractional 0–1 programming and submodularity," Journal of Global Optimization, Springer, vol. 84(1), pages 77-93, September.
    2. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    3. Alfandari, Laurent & Hassanzadeh, Alborz & Ljubic, Ivana, 2020. "An Exact Method for Assortment Optimization under the Nested Logit Model," ESSEC Working Papers WP2001, ESSEC Research Center, ESSEC Business School, revised 2020.
    4. Laurent Alfandari & Alborz Hassanzadeh & Ivana Ljubić, 2021. "An Exact Method for Assortment Optimization under the Nested Logit Model," Working Papers hal-02463159, HAL.

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