Solving the maximum clique problem using a tabu search approach. (English) Zbl 0775.90297


90C35 Programming involving graphs or networks
90C27 Combinatorial optimization
90-08 Computational methods for problems pertaining to operations research and mathematical programming
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[1] G. Avondo-Bodeno,Economic Applications of the Theory of Graphs (Gordon and Breach, New York, 1962).
[2] L. Babel, Finding maximum cliques in arbitrary and in special graphs, Report TUM-M9008, Mathematisches Institut und Institut für Informatik, Technische Universität München (1990), to appear in Computing.
[3] L. Babel and G. Tinhofer, A branch and bound algorithm for the maximum clique problem, Zeits. Oper. Res. 34(1990)207–217. · Zbl 0701.90091
[4] E. Balas and J. Xue, Minimum weighted coloring of triangulated graphs, with application to maximum weight vertex packing and clique finding in arbitrary graphs, SIAM J. Comput. 20(1991)209–221. · Zbl 0722.68086 · doi:10.1137/0220012
[5] E. Balas and C.S Yu, Finding a maximum clique in an arbitrary graph, SIAM J. Comput. 15(1986)1054–1068. · Zbl 0604.05024 · doi:10.1137/0215075
[6] C. Berge,Théorie des Graphes et ses Applications (Dunod, Paris, 1962).
[7] B. Bollobas,Random Graphs (Academic Press, London, 1985).
[8] B. Bollobas and P. Erdös, Cliques in random graphs, Math. Proc. Camb. Phil. Soc. 80(1976)419–427. · Zbl 0344.05155 · doi:10.1017/S0305004100053056
[9] C. Bron and J. Kerbosch, Finding all cliques of an undirected graph, Comm. ACM 16(1973)575–577. · Zbl 0261.68018 · doi:10.1145/362342.362367
[10] R. Carraghan and P.M. Pardalos, An exact algorithm for the maximum clique problem, Oper. Res. Lett. 9(1990)375–382. · Zbl 0711.90080 · doi:10.1016/0167-6377(90)90057-C
[11] V. Degot and J.M. Hualde, De l’utilisation de la notion de clique (sous-graphe complet symétrique) en matière de typologie des populations, Revue française d’automatique et recherche opérationelle: Recherche opérationelle 9(1975)5–18. · Zbl 0303.68028
[12] N. Deo,Graph Theory with Applications to Engineering and Computer Science (Prentice-Hall, Englewood Cliffs, 1974). · Zbl 0285.05102
[13] C. Ebenegger, P.L. Hammer and D. de Werra, Pseudo-Boolean functions and stability of graphs, Ann. Discr. Math. 19(1984)83–98. · Zbl 0567.05031
[14] C. Friden, A Hertz and D. de Werra, Stabulus: a technique for finding stable sets in large graphs with tabu search, Computing 42(1989)35–44. · Zbl 0685.68056 · doi:10.1007/BF02243141
[15] C. Friden, A Hertz and D. de Werra, Tabaris: An exact algorithm based on tabu search for finding a maximum independent set in a graph, Comput. Oper. Res. 17(1990)437–445. · Zbl 0713.90087 · doi:10.1016/0305-0548(90)90048-C
[16] M.R. Garey and D.S. Johnson,Computers and Intractibility: a Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979). · Zbl 0411.68039
[17] M. Gendreau, A fast greedy algorithm for the maximum clique problem, paper presented at the TIMS/ORSA Meeting, New Orleans (May 1987).
[18] M. Gendreau, J.-C. Picard and L. Zubieta, An efficient implicit enumeration algorithm for the maximum clique problem, in:Advances in Optimization and Control ed. H.A. Eiselt and G. Pederzoli (Springer, Berlin, 1988). · Zbl 0648.90083
[19] M. Gendreau, L. Salvail and P. Soriano, An appraisal of greedy heuristics for the maximum clique problem, Centre de Recherche sur les Transports, Université de Montréal, forthcoming.
[20] M. Gendreau, P. Soriano and L. Salvail, Simulated annealing and cliques, Centre de Recherche sur les Transports, Université de Montréal, forthcoming; paper presented at the ORSA/TIMS Meeting, New York (October 1989).
[21] L. Gerhards and W. Lindenberg, Clique detection for nondirected graphs: two new algorithms, Computing 21 (1979)295–322. · Zbl 0441.68073 · doi:10.1007/BF02248731
[22] F. Glover, Future paths for integer programming and links to artificial intelligence, Comput. Oper. Res. 13(1986)533–549. · Zbl 0615.90083 · doi:10.1016/0305-0548(86)90048-1
[23] F. Glover, Tabu search. Part I, ORSA J. Comput. 1(1989)190–206.
[24] F. Glover, Tabu search. Part II, ORSA J. Comput. 2(1990)4–32.
[25] J.W. Greene and K.J. Supowit, Simulated annealing without rejected moves, IEEE Trans. Comput. Aided Des. CAD-5(1986)221–228. · doi:10.1109/TCAD.1986.1270190
[26] M. Grötschel, L. Lovasz and A. Schrijver,Geometric Algorithms and Combinatorial Optimization (Springer, Berlin, 1988). · Zbl 0634.05001
[27] P. Hansen and B. Jaumard, Algorithms for the maximum satisfiability problem, RUTCOR Research Report 43–87, Rutgers University (1987). · Zbl 0716.68077
[28] F. Harary, Graph theory as a structural model in the social sciences, in:Graph Theory and its Applications, ed. B. Harris (Academic Press, New York, 1970). · Zbl 0224.05129
[29] A. Hertz and D. de Werra, Using tabu search techniques for graph coloring, Computing 29(1987)345–351. · Zbl 0626.68051 · doi:10.1007/BF02239976
[30] D.S. Johnson, Approximation algorithms for combinatorial problems, J. Comput. Syst. Sci. 9(1974)256–278. · Zbl 0296.65036 · doi:10.1016/S0022-0000(74)80044-9
[31] D.S. Johnson, M. Yannakakis and C.H. Papadimitriou, On generating all maximal independent sets, Inf. Proc. Lett. 27(1988)119–123. · Zbl 0654.68086 · doi:10.1016/0020-0190(88)90065-8
[32] S. Kirkpatrick, C.D. Gelatt Jr. and M.P. Vecchi, Optimization by simulated annealing, Science 220(1983)671–680. · Zbl 1225.90162 · doi:10.1126/science.220.4598.671
[33] E. Loukakis, A new backtracking algorithm for generating the family of maximal independent sets of a graph, Comput. Math. Appl. 9(1983)583–589. · Zbl 0528.05058 · doi:10.1016/0898-1221(83)90115-3
[34] E. Loukakis and C. Tsouros, Determining the number of internal stability of a graph, Int. J. Comput. Math. 11(1982)207–220. · Zbl 0496.05057 · doi:10.1080/00207168208803311
[35] D.W. Matula, The employee party problem, Not. A.M.S. 19(1972)A-382.
[36] D.W. Matula, The largest clique in a random graph, Technical Report CS7608, Southern Methodist University (1976).
[37] D.W. Matula, Expose-and-merge exploration and the chromatic number of a random graph, Combinatorica 7(1987)275–284. · Zbl 0648.05049 · doi:10.1007/BF02579304
[38] P.M. Pardalos and N. Desai, An algorithm for finding a maximum weighted independent set in arbitrary graph, Int. J. Comput. Math. 38(1991)163–175. · Zbl 0723.68085 · doi:10.1080/00207169108803967
[39] P.M. Pardalos and A. Phillips, A global optimization approach for solving the maximum clique problem, Int. J. Comput. Math. 33((1990)209–216. · Zbl 0825.68488 · doi:10.1080/00207169008803851
[40] P.M. Pardalos and G.P. Rodgers, A branch and bound algorithm for the maximum clique problem, Comp. Oper. Res. 19(1992)363–375. · Zbl 0757.90082 · doi:10.1016/0305-0548(92)90067-F
[41] J.M. Robson, Algorithms for the maximum independent sets, J. Algor. 7(1986)425–440. · Zbl 0637.68080 · doi:10.1016/0196-6774(86)90032-5
[42] B. Roy,Algèbre Moderne et Théorie des Graphes, Vol. 1 (Dunod, Paris, 1969). · Zbl 0238.90072
[43] C.E. Shannon, The zero-error capacity of a noisy channel,Symp. on Information Theory, I.R.E. Trans. 3(1956).
[44] R.E. Tarjan and A.E. Trojanowski, Finding a maximum independent set, SIAM J. Comput. 6(1977)537–546. · Zbl 0357.68035 · doi:10.1137/0206038
[45] J. Turner and W.H. Kautz, A survey of progress in graph theory in the Soviet Union, SIAM 12(1970). · Zbl 0201.56702
[46] D. de Werra and A. Hertz, Tabu search techniques: A tutorial and application to neural networks, OR Spektrum 11(1989)131–141. · Zbl 0672.90089 · doi:10.1007/BF01720782
[47] M. Widmer and A. Hertz, A new heuristic method for solving the flow shop sequencing problem, Eur. J. Oper. Res. 41(1989)186–193. · Zbl 0671.90040 · doi:10.1016/0377-2217(89)90383-4
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