Graph k-colorability through threshold accepting and Davis-Putnam

Authors:
Juan Frausto-Solís;Héctor Sanvicente-Sanchez;Marco Antonio Cruz-Chavez;Mónica Larre Bolaños-Cacho;José Crispín Zavala-Díaz;Huberto Ayanegui
Affiliations:
Department of Computer Science, ITESM, Temixco, Morelos, México;Instituto Mexicano de Tecnología del Agua, Jiutepec, Morelos, México;Engineering and Applied Science Research Center, UAEM, Cuernavaca, Morelos, México;Department of Computer Science, ITESM, Temixco, Morelos, México;Engineering and Applied Science Research Center, UAEM, Cuernavaca, Morelos, México;Department of Computer Science, ITESM, Temixco, Morelos, México
Venue:
CIMMACS'05 Proceedings of the 4th WSEAS international conference on Computational intelligence, man-machine systems and cybernetics
Year:
2005

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Abstract

The Graph k-Colorability Problem (GCP) is a well known NP-hard problem consisting on finding the k minimum number of colors to paint the vertexes of a graph in such a way that two any vertexes joined by an edge has always different colors. Many years ago, Simulated Annealing (SA) was used for graph coloring obtaining good results; however SA is not a complete algorithm and so not always gets the optimal solution. In this paper GCP is transformed into the Satisfiability Problem and then it is solved using a hybrid algorithm that uses the Threshold Accepting algorithm (a variant of SA) and the classical one literal rule of Davis & Putnam. The new algorithm is a complete one and so gets better quality that the classical simulated annealing algorithm.