Abstract
In this paper a new sorting strategy is proposed to be used in the maximum weight clique finding algorithm, which is known to be the fastest at the moment. It is based on colour classes, i.e. on heuristic colouring that is used to prune efficiently branches by excluding from the calculation formulae vertices of the same colours. That is why the right ordering before colouring is so crucial before executing the heuristic colouring and consequently the main maximum weight clique searching routine. Computational experiments with random graphs were conducted and have shown a sufficient increase of performance considering the type of application dealt with in the article.
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References
MacWilliams, J., Sloane, N.J.A.: The theory of error correcting codes. North-Holland, Amsterdam (1979)
Corradi, K., Szabo, S.: A combinatorial approach for Keller’s Conjecture. Periodica Mathematica Hungarica 21, 95–100 (1990)
Berman, P., Pelc, A.: Distributed fault diagnosis for multiprocessor systems. In: 20th Annual International Symposium on Fault-Tolerant Computing, Newcastle, UK, pp. 340–346 (1990)
Horaud, R., Skordas, T.: Stereo correspondence through feature grouping and maximal cliques. IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 1168–1180 (1989)
Mitchell, E.M., Artymiuk, P.J., Rice, D.W., Willet, P.: Use of techniques derived from graph theory to compare secondary structure motifs in proteins. Journal of Molecular Biology 212, 151–166 (1989)
Jansen, K., Scheffler, P., Woeginger, G.: The disjoint cliques problem. Operations Research 31, 45–66 (1997)
Bomze, M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: Handbook of Combinatorial Optimization 4. Kluwer Academic Publishers, Boston (1999)
Carraghan, R., Pardalos, P.M.: A parallel algorithm for the maximum weight clique problem. Technical report CS-90-40, Dept of Computer Science, Pennsylvania State University (1990)
Carraghan, R., Pardalos, P.M.: An exact algorithm for the maximum clique problem. Op. Research Letters 9, 375–382 (1990)
Ostergard, P.R.J.: A new algorithm for the maximum-weight clique problem. Nordic Journal of Computing 8, 424–436 (2001)
Johnson, D.S., Trick, M.A. (eds.): Cliques, Colouring and Satisfiability: Second DIMACS Implementation Challenge. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26. American Mathematical Society (1996)
Kumlander, D.: Some practical algorithms to solve the maximum clique problem. Tallinn University of Technology Press, Tallinn (2005)
Kumlander, D.: Network resources for the maximum clique problem, http://www.kumlander.eu/graph
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Kumlander, D. (2008). On Importance of a Special Sorting in the Maximum-Weight Clique Algorithm Based on Colour Classes. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. MCO 2008. Communications in Computer and Information Science, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87477-5_18
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DOI: https://doi.org/10.1007/978-3-540-87477-5_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87476-8
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