Abstract
The article deals with an evolutionary based method to decompose graph into strongly connected structures, we called α-cliques. The α-clique is a generalization of a clique concept with the introduction of parameter α. Using this parameter it is possible to control the degree (or strength) of connections among vertices (nodes) of this sub-graph structure. The evolutionary approach is proposed as a method that enables to find separate α-cliques that cover the set of graph vertices.
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References
Altus S S, Kroo I M, Gage P J, (1996) Genetic Algorithm for Scheduling and Decomposition of Multidisciplinary Design Problems. Journal of Mechanical Design, Vol. 118, No. 4.
Bagirov A M, Yearwood J. (2006) A new non-smooth optimization algorithm for minimum sum-of-squares clustering problems, Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, P.O. Box 663, Vic. 3353, Australia.
Benson S J, Ye Y, (2000) Approximating maximum stable set and minimum graph coloring problems with the positive semi-definite relaxation, Computational complexity: The problem of approximation, Kluwer Academic Publishers.
Browning T R, (2001) Applying the Design Structure Matrix to System Decomposition and Integration Problems: A Review and New Directions, IEEE Transactions on Engineering Management, Vol. 48, No 3.
Cichosz P, (2000) Systemy uczźce siê (in Polish), WNT, Warszawa.
Hansen P, Mladenovic N, Urosevic D, (2004) Variable neighborhood search for the maximum clique The Fourth International Colloquium on Graphs and Optimisation (GO-IV)GO-IV International Colloquium on Graphs and Optimisation No4, Loeche-les-Bains, SUISSE (20/08/2000), vol. 145, no 1 (28 ref.), pp. 117–125.
Hassin R, Khuller S, (1986) z-Approximation, Computational complexity: The problem of approximation, New York.
Jukna S, (2001) Extremal Combinatorics, Springer-Verlag Berlin Heidelberg.
ăKloks T, ăKratsch D, (1998) Listing all minimal separators of a graph, SIAM J. COMPUT. Vol. 27, No. 3, pp. 605–613.
Kumlander D, (2007) An Approach for the Maximum Clique Finding Problem Test Tool Software Engineering, Software Engineering, SE 2007, Innsbruck, Austria
Lenstra J K, (1997) Sequencing by Enumerative Methods, Mathematisch Centrum, Amsterdam.
McCulley C, Bloebaum C A, (1996) Genetic tool for optimal design sequencing in complex engineering systems, Structural Optimization, Vol. 12, No. 2–3.
Owsihski J W, (1990) On a new naturally indexed quick clustering method with a global objective function, Applied Stochastic Models and Data Analysis, Vol. 6.
Potrzebowski H. Stańczak J, Sep K, (2004) Evolutionary method in grouping of units with argument reduction, Proceedings of the 15th International Conference on Systems Science, ed. Z. Bubnicki, A. Grzech, vol. III, pp. 29–36.
Potrzebowski H. Stahczak J, Sep K,(2005) Evolutionary method in grouping of units Proceedings of the 4th International Conference on Recognition Systems CORESŠ05, Springer-Verlag, Berlin-Heidelberg.
Potrzebowski H. Stahczak J, Sep K, (2006) Evolutionary Algorithm to Find Graph Covering Subsets Using α-Cliques, Praca zbiorowa pod red. J.Arabasa: Evolutionary Computation and Global Optimization, 351–358. Prace naukowe Politechniki Warszawskiej.
Potrzebowski H. Stahczak J, Sep K, (2006) Heurystyczne i ewolucyjne metody znajdowania pokrycia grafu, korzystajace z pojecia alfa-kliki i innych ograniczeh (in Polish), Badania operacyjne i systemowe 2006. Metody i techniki, Akademicka Oficyna Wydawnicza EXIT, Warszawa.
ăProtasi M, (2001) Reactive local search for the maximum clique problem, Algoritmica vol. 29, no 4. pp. 610–637.
ăRogers J L, (1997) Reducing Design Cycle Time and Cost Thorough Process Resequencing, International Conference on Engineering Design ICED 1997, Tampere, Finland.
Syslo M M, Deo N, Kowalik J S, (1983) Algorithms of discrete optimization, Prentice-Hall.
Stańczak J, (2003) Biologically inspired methods for control of evolutionary algorithms, Control and Cybernetics, 32(2), pp. 411–433.
Wilson R J, (1996) Introduction to graph theory Addison Wesley Longman.
Yu T L, Goldberg D E, Yassine A, Yassine C A, (2003) Genetic algorithm design inspired by organizational theory, Genetic and Evolutionary Computation Conference Chicago, Illinois, USA, Publ. Springer-Verlag, Heidelberg, Lecture Notes in Computer Science, Vol. 2724/2003.
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Potrzebowski, H., Stańczak, J., Scep, K. (2007). Separable Decomposition of Graph Using α-cliques . In: Kurzynski, M., Puchala, E., Wozniak, M., Zolnierek, A. (eds) Computer Recognition Systems 2. Advances in Soft Computing, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75175-5_49
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DOI: https://doi.org/10.1007/978-3-540-75175-5_49
Publisher Name: Springer, Berlin, Heidelberg
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