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A discrete dynamic convexized method for the max-cut problem

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  • Geng Lin
  • Wenxing Zhu

Abstract

The max-cut problem is a classical NP-hard problem in graph theory. In this paper, we adopt a local search method, called MCFM, which is a simple modification of the Fiduccia-Mattheyses heuristic method in Fiduccia and Mattheyses (Proc. ACM/IEEE DAC, pp. 175–181, 1982 ) for the circuit partitioning problem in very large scale integration of circuits and systems. The method uses much less computational cost than general local search methods. Then, an auxiliary function is presented which has the same global maximizers as the max-cut problem. We show that maximization of the function using MCFM can escape successfully from previously converged discrete local maximizers by taking increasing values of a parameter. An algorithm is proposed for the max-cut problem, by maximizing the auxiliary function using MCFM from random initial solutions. Computational experiments were conducted on three sets of standard test instances from the literature. Experimental results show that the proposed algorithm is effective for the three sets of standard test instances. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Geng Lin & Wenxing Zhu, 2012. "A discrete dynamic convexized method for the max-cut problem," Annals of Operations Research, Springer, vol. 196(1), pages 371-390, July.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:371-390:10.1007/s10479-012-1133-2
    DOI: 10.1007/s10479-012-1133-2
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    References listed on IDEAS

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    1. Ling, Ai-Fan & Xu, Cheng-Xian & Xu, Feng-Min, 2009. "A discrete filled function algorithm embedded with continuous approximation for solving max-cut problems," European Journal of Operational Research, Elsevier, vol. 197(2), pages 519-531, September.
    2. Francisco Barahona & Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1988. "An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design," Operations Research, INFORMS, vol. 36(3), pages 493-513, June.
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    Cited by:

    1. Fuda Ma & Jin-Kao Hao, 2017. "A multiple search operator heuristic for the max-k-cut problem," Annals of Operations Research, Springer, vol. 248(1), pages 365-403, January.
    2. Geng Lin & Wenxing Zhu & M. Montaz Ali, 2016. "An effective discrete dynamic convexized method for solving the winner determination problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 563-593, August.

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