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.
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This research was supported partially by the National Natural Science Foundation of China under Grants 10931003 and 61170308, the National Key Basic Research Special Foundation (NKBRSF) of China under Grant 2011CB808000, the Research Fund for the Doctoral Program (RFDP) of China under Grant 20093514110004, and the Science and Technology Project of the Education Bureau of Fujian, China, under Grant JA11201.
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Lin, G., Zhu, W. A discrete dynamic convexized method for the max-cut problem. Ann Oper Res 196, 371–390 (2012). https://doi.org/10.1007/s10479-012-1133-2
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DOI: https://doi.org/10.1007/s10479-012-1133-2