A complementary pivoting approach to the maximum weight clique problem

SIAM Journal on Optimization

Volumn 12, Issue 4, 2002, Pages 928-948

  Massaro, Alessio ^a   Pelillo, Marcello ^a   Bomze, Immanuel M ^a  

^a Thermo Fisher Scientific   (United States)

Author keywords

Combinatorial optimization; Heuristics; Linear complementarity; Maximum weight clique; Pivoting methods; Quadratic programming

Indexed keywords

EID: 0036435029     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623400381413     Document Type: Article

References (30)

1. L. Babel, A fast algorithm for the maximum weight clique problem, Computing, 52 (1994), pp. 31-38.
2. I.M. Bomze, Copositivity conditions for global optimality in indefinite quadratic programming problems, Czech. J. Oper. Res., 1 (1992), pp. 7-19.
3. I.M. Bomze, On standard quadratic optimization problems, J. Global Optim., 13 (1998), pp. 369-387.
4. I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo, The maximum clique problem, in Handbook of Combinatorial Optimization-Suppl. Vol. A, D.-Z. Du and P.M. Pardalos, eds., Kluwer Academic Publishers, Boston, MA, 1999, pp. 1-74.
5. I.M. Bomze, M. Budinich, M. Pelillo, and C. Rossi, Annealed replication: A new heuristic for the maximum clique problem, Discrete Appl. Math., 2002, to appear.
6. I.M. Bomze, M. Pelillo, and R. Giacomini, Evolutionary approach to the maximum clique problem: Empirical evidence on a larger scale, in Developments in Global Optimization, I.M. Bomze, T. Csendes, R. Horst, and P.M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997, pp. 95-108.
7. I.M. Bomze, M. Pelillo, and V. Stix, Approximating the maximum weight clique using replicator dynamics, IEEE Trans. Neural Networks, 11 (2000), pp. 1228-1241.
8. R. Boppana and M. Halldórsson, Approximating maximum independent sets by excluding subgraphs, BIT, 32 (1992), pp. 180-196.
9. M. Brockington and J.C. Culberson, Camouflaging independent sets in quasi-random graphs, in Cliques, Coloring and Satisfiability, D. Johnson and M.A. Trick, eds., DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 26, AMS, Providence, RI, 1996, pp. 75-88.
10. K. Corrádi and S. Szabó, A combinatorial approach for Keller's conjecture, Period. Math. Hungar., 21 (1990), pp. 95-100.
11. R.W. Cottle, J. Pang, and R.E. Stone, The Linear Complementarity Problem, Academic Press, Boston, MA, 1992.
12. L.E. Gibbons, D.W. Hearn, and P.M. Pardalos, A continuous-based heuristic for the maximum clique problem, in Cliques, Coloring and Satisfiability, D. Johnson and M.A. Trick, eds., DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 26, AMS, Providence, RI, 1996, pp. 103-124.
13. L.E. Gibbons, D.W. Hearn, P.M. Pardalos, and M.V. Ramana, Continuous characterizations of the maximum clique problem, Math. Oper. Res., 22 (1997), pp. 754-768.
14. T. Grossman, Applying the INN model to the maximum clique problem, in Cliques, Coloring and Satisfiability, D. Johnson and M.A. Trick, eds., DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 26, AMS, Providence, RI, 1996, pp. 125-145.
15. J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, UN, 1998.
16. S. Homer and M. Peinado, Experiments with polynomial-time CLIQUE approximation algorithms on very large graphs, in Cliques, Coloring and Satisfiability, D. Johnson and M.A. Trick, eds., DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 26, AMS, Providence, RI, 1996, pp. 147-167.
17. R. Horaud and T. Skordas, Stereo correspondence through feature grouping and maximal cliques, IEEE Trans. Pattern Anal. Machine Intell., 11 (1989), pp. 1168-1180.
18. A. Jagota, L. Sanchis, and R. Ganesan, Approximately solving maximum clique using neural network and related heuristics, in Cliques, Coloring and Satisfiability, D. Johnson and M.A. Trick, eds., DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 26, AMS, Providence, RI, 1996, pp. 169-204.
19. D. Johnson and M.A. Trick, eds., Cliques, Coloring and Satisfiability: Second DIMACS Implementation Challenge, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 26, AMS, Providence, RI, 1996.
20. A. Kuznetsova AND A. Strekalovsky, On solving the maximum clique problem, J. Global Optim., 21 (2001), pp. 265-288.
21. A. Massaro and M. Pelillo, A complementary pivoting approach to graph matching, in Energy Minimization Methods in Computer Vision and Pattern Recognition, M. Figueiredo, J. Zerubia, and A.K. Jain, eds., Lecture Notes in Comput. Sci. 2134, Springer-Verlag, Berlin, 2001, pp. 469-479.
22. A. Menon, K. Mehrotra, C.K. Mohan, and S. Ranka, Optimization using replicators, in Proceedings of the 6th International Conference on Genetic Algorithms, Pittsburg, PA, 1995, Morgan Kaufmann, San Francisco, CA, pp. 209-216.
23. D.A. Miller and S.W. Zucker, Efficient simplex-like methods for equilibria of nonsymmetric analog networks, Neural Computation, 4 (1992), pp. 167-190.
24. T.S. Motzkin and E.G. Straus, Maxima for graphs and a new proof of a theorem of Turán, Canad. J. Math., 17 (1965), pp. 533-540.
25. K.G. Murty and S.N. Kabadi, Some NP-complete problems in quadratic and linear programming, Math. Programming, 39 (1987), pp. 117-129.
26. M. Pelillo, Replicator dynamics in combinatorial optimization, in Encyclopedia of Optimization, C.A. Floudas and P.M. Pardalos, eds., Kluwer Academic Publishers, Boston, MA, 2001.
27. M. Pelillo and A. Jagota, Feasible and infeasible maxima in a quadratic program for the maximum clique problem, J. Artificial Neural Networks, 2 (1995), pp. 411-420.
28. M. Pelillo, K. Siddiqi, and S.W. Zucker, Matching hierarchical structures using association graphs, IEEE Trans. Pattern Anal. Machine Intell., 21 (1999), pp. 1105-1120.
29. L. Sanchis, Test case construction for the vertex cover problem, in Computational Support for Discrete Mathematics, N. Dean and G.E. Shannon, eds., DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 15, AMS, Providence, RI, 1994, pp. 315-326.
30. P. Soriano and M. Gendreau, Tabu search algorithms for the maximum clique problem, in Cliques, Coloring and Satisfiability, D. Johnson and M.A. Trick, eds., DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 26, AMS, Providence, RI, 1996, pp. 221-242.