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A Heuristic for the Maximum Independent Set Problem Based on Optimization of a Quadratic Over a Sphere

Author

Listed:
  • Stanislav Busygin

    (Contentsoft AG)

  • Sergiy Butenko

    (University of Florida)

  • Panos M. Pardalos

    (Contentsoft AG)

Abstract

For a given graph the maximum independent set problem is to find a maximum subset of vertices no two of which are adjacent. We propose a heuristic for the maximum independent set problem which utilizes classical results for the problem of optimization of a quadratic function over a sphere. The efficiency of the approach is confirmed by results of numerical experiments on DIMACS benchmarks.

Suggested Citation

  • Stanislav Busygin & Sergiy Butenko & Panos M. Pardalos, 2002. "A Heuristic for the Maximum Independent Set Problem Based on Optimization of a Quadratic Over a Sphere," Journal of Combinatorial Optimization, Springer, vol. 6(3), pages 287-297, September.
    • Handle: RePEc:spr:jcomop:v:6:y:2002:i:3:d:10.1023_a:1014899909753
    DOI: 10.1023/A:1014899909753
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    References listed on IDEAS

    as
    1. Luana E. Gibbons & Donald W. Hearn & Panos M. Pardalos & Motakuri V. Ramana, 1997. "Continuous Characterizations of the Maximum Clique Problem," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 754-768, August.
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    Cited by:

    1. Qinghua Wu & Jin-Kao Hao, 2013. "An adaptive multistart tabu search approach to solve the maximum clique problem," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 86-108, July.
    2. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2018. "A nonconvex quadratic optimization approach to the maximum edge weight clique problem," Journal of Global Optimization, Springer, vol. 72(2), pages 219-240, October.
    3. Balabhaskar Balasundaram & Sergiy Butenko & Svyatoslav Trukhanov, 2005. "Novel Approaches for Analyzing Biological Networks," Journal of Combinatorial Optimization, Springer, vol. 10(1), pages 23-39, August.
    4. Benjamin McClosky & Illya V. Hicks, 2012. "Combinatorial algorithms for the maximum k-plex problem," Journal of Combinatorial Optimization, Springer, vol. 23(1), pages 29-49, January.

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