Simple ingredients leading to very efficient heuristics for the maximum clique problem

Journal of Heuristics

Volumn 14, Issue 6, 2008, Pages 587-612

  Grosso, Andrea ^a   Locatelli, Marco ^a   Pullan, Wayne ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b GRIFFITH UNIVERSITY   (Australia)

Author keywords

Maximum clique; Penalties; Plateau search; Randomness; Restart rules

Indexed keywords

HEURISTIC METHODS; LEARNING ALGORITHMS; PROBLEM SOLVING;

MAXIMUM CLIQUE; PENALTIES; PLATEAU SEARCH; RANDOMNESS; RESTART RULES;

ALGORITHMS;

EID: 58449085212     PISSN: 13811231     EISSN: 15729397     Source Type: Journal    
DOI: 10.1007/s10732-007-9055-x     Document Type: Article

References (31)

1. R. Battiti M. Protasi 2001 Reactive local search for the maximum clique problem Algorithmica 29 4 610 637
2. M. Bellare O. Goldreich M. Sudan 1998 Free bits, PCPs, and nonapproximability-towards tight results SIAM J. Comput. 27 3 804 915
3. Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, suppl. vol. A, pp. 1-74 (1999)
4. I.M. Bomze M. Pelillo V. Stix 2000 Approximating the maximum weight clique using replicator dynamic IEEE Trans. Neural Netw. 11 6 1228 1241
5. Brockington, M., Culberson, J.C.: Camouflaging independent sets in quasi-random graphs, in Johnson and Trick (1996)
6. S. Burer R.D.C. Monteiro Y. Zhang 2002 Maximum stable set formulations and heuristics based on continuous optimization Math. Prog. 94 137 166
7. S. Busygin 2006 A new trust region technique for the maximum clique problem Discrete Appl. Math. 154 2080 2096
8. E. de Klerk D.V. Pasechnik 2002 Approximation of the stability number of a graph via copositive programming SIAM J. Optim. 12 875 892
9. Dukanovic, I., Rendl, F.: Semidefinite programming relaxations for graph coloring and maximal clique problems. Working paper, Univ. of Klagenfurt, available at http://www.optimization-online.org/DB-HTML/2005/03/1081.html (2005)
10. Fahle, T.: Simple and fast: improving a branch-and-bound algorithm for maximum clique. LNCS, vol. 2461, pp. 485-498 (2002)
11. Garey, M., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. Wiley, New York (1977)
12. A. Grosso M. Locatelli F. Della Croce 2004 Combining swaps and node weights in an adaptive greedy approach for the maximum clique problem J. Heuristics 10 135 152
13. Grosso, A., Locatelli, M., Pullan, W.J.: Short communication, larger cliques for a DIMACS test. http://www.optimization-online.org/DB-HTML/2005/02/ 1054.html (2005)
14. Gvozdenovic, N., Laurent, M.: Semidefinite bounds for the stability number of a graph via sums of squares of polynomials. In: Integer Programming and Combinatorial Optimization: 11th International IPCO Conference. Lecture Notes in Computer Science, vols. 3509/2005, pp. 136-151. (2005)
15. P. Hansen N. Mladenović D. Urošević 2004 Variable neighborhood search for the maximum clique Discrete Appl. Math. 145 117 125
16. A. Jagota L.A. Sanchis 2001 Adaptive, restart, randomized greedy heuristics for maximum clique J. Heuristics 7 565 585
17. Johnson, D.S., Trick, M. (eds.): Cliques, Coloring and Satisfiability: Second DIMACS Implementation Challenge. DIMACS Series, vol. 26. American Mathematical Society, Providence (1996)
18. K. Katayama A. Hamamoto H. Narihisa 2005 An effective local search for the maximum clique problem Inform. Process. Lett. 95 503 511
19. P.R.J. Östergard 2002 A fast algorithm for the maximum clique problem Discrete Appl. Math. 120 197 207
20. J.B. Lasserre 2001 Global optimization with polynomials and the problem of moments SIAM J. Optim. 11 796 817
21. A. Massaro M. Pelillo I.M. Bomze 2002 A complementary pivoting approach to the maximum weight clique problem SIAM J. Optim 12 4 928 948
22. Pena, J., Vera, J., Zuluaga, L.: Computing the stability number of a graph via linear and semidefinite programming. Working Paper, Tepper School of Business, Carnegie Mellon Univ., available at http://www.optimization-online. org/DB-HTML/2005/04/1106.html (2005)
23. W.J. Pullan H.H. Hoos 2006 Dynamic local search for the maximum clique problem J. Artif. Intell. Res. 25 159 185
24. Regin, J.-C.: Solving the maximum clique problem with constraint programming. In: LNCS, vol. 2883, pp. 634-648 (2003)
25. L. Sanchis A. Jagota 1996 Some experimental and theoretical results on test case generators for the maximum clique problem INFORMS J. Comput. 8 2 87 102
26. SAT'04 Competition, http://www.lri.fr/~simon/contest04/results/ (2004)
27. A. Schrijver 1979 A comparison of the Delsarte and Lovasz bounds IEEE Trans. Inform. Theory 25 425 429
28. Shinano, Y., Fujie, T., Ikebe, Y., Hirabayashi, R.: Solving the maximum clique problem using PUBB. In: Proceedings 12th IPPS/ 9th SPDP, pp. 326-332 (1998)
29. A. Singh A.K. Gupta 2006 A hybrid heuristics for the maximum clique problem J. Heuristics 12 5 22
30. C. Solnon S. Fenet 2006 A study of ACO capabilities for solving the maximum clique problem J. Heuristics 12 155 180
31. D.R. Wood 1997 An algorithm for finding a maximum clique in a graph Oper. Res. Lett. 21 5 211 217