Finding All Maximal Cliques in Dynamic Graphs
- Volker Stix
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Clustering applications dealing with perception based or biased data lead to models with non-disjunct clusters. There, objects to be clustered are allowed to belong to several clusters at the same time which results in a fuzzy clustering. It can be shown that this is equivalent to searching all maximal cliques in dynamic graphs like G t = (V,E t), where E t − 1 ⊂ E t, t = 1,...,T; E 0 = φ. In this article algorithms are provided to track all maximal cliques in a fully dynamic graph.
- B. Bollobás, Modern Graph Theory. Springer: New York, 1998.
- I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo, “The maximum clique problem,” in Handbook of Combinatorial Optimization, volume Suppl. vol. A:4, Kluwer Academic Publishers: Boston, MA, 1999.
- I.M. Bomze and V. Stix, “Genetic engineering via negative fitness: Evolutionary dynamics for global optimization,” Annals of Oper. Res., vol. 89, pp. 297–318, 1999.
- C. Bron and J. Kerbosch, “Algorithm 457: Finding all cliques of an undirected graph,” Commun. ACM, vol. 16, no. 9, pp. 575–577, 1973.
- M. Broom, C. Cannings, and G. T. Vickers, “On the number of local maxima of a constrained quadratic form,” Proc. R. Soc. Lond., vol. 443, pp. 573–584, 1993.
- E. Cambouropoulos, A. Smaill, and G. Widmer, “A clustering algorithm for melodic analysis,” in Proceedings of the Diderot'99, 1999.
- E. Cambouropoulos and G. Widmer, “Melodic clustering: Motivic analysis of Schumann's Träumerei,” in Proceedings of JIM 2000, Bordeaux, 2000.
- C. Cannings and G.T. Vickers, “Patterns of ESSs II,” J. Theor. Biol., vol. 132, pp. 409–420, 1988.
- D. Eppstein, “Clustering for faster network simplex pivots,” in Proc. 5th ACM-SIAM Symp. Discrete Algorithms, 1994, pp. 160–166.
- D. Eppstein, Z. Galil, and G.F. Italiano, Algorithms and Theory of Computation Handbook, chapter Dynamic Graph Algorithms. CRC Press: New York, 1999, pp. 8-1–8-25.
- Z. Galil and G.F. Italiano, “Fully dynamic algorithms for 2-edge-connectivity,” SIAM J. Comput., vol. 21, pp. 1047–1069, 1992.
- E.J. Gardiner, P.J. Artymiuk, and P. Willett, “Clique-detection algorithms for matching three-dimensional molecular structures,” Journal of Molecular Graphics and Modelling, vol. 15, no. 4, pp. 245–253, 1997.
- M.A. Gluck and J.E. Corter, “Information, uncertainty, and the utility of categories,” in Proc. 7th Ann. Conf. of the Cognitive Science Society, 1985.
- J. A. Hartigan, Clustering Algorithms, Wiley Series in Probability and Mathematical Statistics. Wiley: New York, 1975.
- M.R. Henzinger and V. King, “Maintaining minimum spanning trees in dynamic graphs,” in Proc. 24th Int. Coll. Automata, Languages and Programming, 1997, pp. 594–604.
- D.S. Johnson and M.A. Tricks (Eds.), “Cliques, coloring and satisfiability: Second dimacs implementation challenge,” DIMACS Series in Discrete Mathematics and Theoretical Computer Science 26, American Mathematical Society, Procidence, 1996.
- G. Li, V. Uren, E. Motta, S.B. Shum, and J. Domingue, “Claimaker: Weaving a semantic web of research papers,” in 1st International Semantic Web Conference, 2002.
- J.W. Moon and L. Moser, “On cliques in graphs,” Isr. J. Math., vol. 3, pp. 23–28, 1965.
- T.S. Motzkin and E.G. Straus, “Maxima for graphs and a new proof of a theorem of Turán,” Canad. J. Math., vol. 17, no. 4, pp. 533–540, 1965.
- G.T. Vickers and C. Cannings, “Patterns of ESSs I,” J. Theor. Biol., vol. 132, pp. 387–408, 1988.
- Finding All Maximal Cliques in Dynamic Graphs
Computational Optimization and Applications
Volume 27, Issue 2 , pp 173-186
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
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- maximal clique
- dynamic graphs
- fuzzy clustering
- Industry Sectors
- Volker Stix (1)
- Author Affiliations
- 1. Department of Information Business, Vienna University of Economics, Augasse 2–6, A-1090, Vienna/, Austria