Variable neighborhood search for the maximum clique

Discrete Applied Mathematics

Volumn 145, Issue 1 SPEC. ISS., 2004, Pages 117-125

  Hansen, Pierre ^a   Mladenović, Nenad ^a,b   Urošević, Dragan ^b  

^a HEC MONTRÉAL   (Canada)

^b MATHEMATICAL INSTITUTE   (Serbia)

Author keywords

Combinatorial optimization; Graphs; Heuristics; Maximum clique; Variable neighborhood search

Indexed keywords

APPROXIMATION THEORY; GRAPH THEORY; HEURISTIC METHODS; INTEGER PROGRAMMING; NONLINEAR PROGRAMMING; OPTIMIZATION;

CLASSICAL PROBLEMS; COMBINATORIAL OPTIMIZATION; MAXIMUM CLIQUE; VARIABLE NEIGHBOURHOOD SEARCH;

COMBINATORIAL MATHEMATICS;

EID: 4944245585     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2003.09.012     Document Type: Conference Paper

References (28)

1. Aggarwal C., Orlin J., Tai R. Optimized crossover for the independent set problem. Oper. Res. 45:1997;226-234.
2. Babel L., Tinhofer G. A branch and bound algorithm for the maximum clique problem. Zeits. Oper. Res. 34:1990;207-217.
3. T. Bäck, S. Khuri, An evolutionary heuristic for the maximum independent set problem, in: Proceedings of the first IEEE Conference on Evolutionary Computation, IEEE Press, New York, 1994, pp. 531-535.
4. Balas E., Niehaus W. Optimized crossover-based genetic algorithms for the maximum cardinality and maximum weight clique problem. J. Heuristics. 4:1998;107-122.
5. Balas E., Yu C.S. Finding a maximum clique in an arbitrary graph. SIAM J. Comput. 15(4):1986;1054-1068.
6. Battiti R., Protasi M. Reactive local search for the maximum clique problem. Algorithmica. 29:2001;610-637.
7. Bomze I., Budinich M., Pardalos P., Pelillo M. The maximum clique problem. Du D.Z., Pardalos P.M. Handbook of Combinatorial Optimization. 1999;Kluwer Academic Publishers, Dordrecht.
8. Carraghan R., Pardalos P.M. An exact algorithm for the maximum clique problemi. Oper. Res. Lett. 9:1990;375-382.
9. Feo T., Resende M., Smith S. A greedy randomized adaptive search procedure for maximum independent set. Oper. Res. 42:1994;860-878.
10. Friden C., Hertz A., de Werra D. Tabaris. an exact algorithm based on tabu search for finding a maximum independent set in a graph Comput. Oper. Res. 17:1990;437-445.
11. Garey M., Johnson D. Computers and Intractability. 1979;Freeman, New York.
12. Gendreau M., Salvail L., Soriano P. Solving the maximum clique problem using a tabu search approach. Ann. Oper. Res. 41:1993;385-403.
13. L.E. Gibbons, D.W. Hearn, P.M. Pardalos, Continuous based heuristic for the Maximum Clique Problemi, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 26, 1996, pp. 103-124.
14. Glover F. Tabu search, Part i. ORSA J. Comput. 1:1989;190-206.
15. Hansen P., Jaumard B. Algorithms for the maximum satisfiability problem. Comput. 44:1990;279-303.
16. P. Hansen, N. Mladenović, Two algorithms for maximum cliques in dense graphs, Technical Report GERAD Research Report G-92-18, 1992.
17. Hansen P., Mladenović N. A comparison of algorithms for the maximum clique problem. Yugoslav J. Oper. Res. 2:1992;3-13.
18. Hansen P., Mladenović N. An introduction to variable neighborhood search. Voss S. Metaheuristics, Advances and Trends in Local Search Paradigms for Optimization. 1999;433-458 Kluwer Academic Publishers, Dordrecht.
19. Hansen P., Mladenović N. Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130:2001;449-467.
20. Johnson D. Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9:1974;256-278.
21. D. Johnson, M. Trick, Cliques, Coloring and Satisfiability: Second Dimacs Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 26.
22. Mladenović N., Hansen P. Variable neighborhood search. Comput. Oper. Res. 24:1997;1097-1100.
23. Motzin T.S., Strauss E.G. Maxima for graphs and a new proof of a theorem of turan. Can. J. Math. 17:1965;533-540.
24. I.H. Osman, G. Laporte, Metaheuristics: a bibliography, in: G. Laporte, I.H. Osman (Eds.), Metaheuristics in Combinatorial Optimization, Ann. Oper. Research 63 (1996) 513-623.
25. Pardalos P., Rodgers G. A branch and bound algorithm for the maximum clique problem. J. Algorithms. 7:1986;425-440.
26. Pardalos P., Xue J. The maximum clique problem. J. Global Opt. 4:1994;301-328.
27. P. Soriano, M. Gendreau, Tabu search algorithms for the maximum clique problem, in: D. Johnson, M. Trick (Eds.), Clique, Coloring and Satisfiability, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 26, American Mathematical Society, Providence, RI, 1966, pp. 221-244.
28. Tomita E., Imamatsu K., Kohata Y., Wakatsuki M. A simple and efficient branch and bound algorithm for finding a maximum clique with experimental evaluations. Syst. Comput. Japan. 28(5):1997;60-67.