Augmentation algorithm for the maximum weighted stable set problem

Computational Optimization and Applications

Volumn 14, Issue 3, 1999, Pages 367-381

  Mannino, Carlo ^a   Stefanutti, Egidio ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; HEURISTIC METHODS; PROBLEM SOLVING; SET THEORY; STATISTICAL METHODS;

AUGMENTATION ALGORITHMS; LOVASZ-PLUMMER CLIQUE REDUCTION METHODS; TABU-SEARCH HEURISTICS;

OPTIMIZATION;

EID: 0032595816     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026456624746     Document Type: Article

References (30)

1. L. Babel, "Finding maximum cliques in arbitrary and special graphs," Computing, vol. 46, no. 4, pp. 321-341, 1991.
2. L. Babel, "A fast algorithm for the maximum weight clique problem," Computing, vol. 52, pp. 31-38, 1994.
3. L. Babel and G. Tinhofer, "A branch and bound algorithm for the maximum clique problem," ZOR-Methods and Models of Operations Research, vol. 34, pp. 207-217, 1990.
4. E. Balas and W. Niehaus, "Finding large clique in arbitrary graphs by bipartite matching," in Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, D.S. Johnson and M.A. Trick (Eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 29-51, American Mathematical Society, 1996.
5. 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 Journal on Computing, vol. 20, pp. 209-221, 1991.
6. E. Balas and J. Xue, "Weighted and unweighted maximum clique algorithms with upper bounds from fractional coloring." Algorithmica, vol. 15, pp. 397-412, 1996.
7. E. Balas and C.S. Yu, "Finding a maximum clique in an arbitrary graph," SIAM Journal on Computing, vol. 15, pp. 1054-1068, 1986.
8. R. Battiti and G. Tecchiolli, "The reactive tabu search," ORSA Journal on Computing , vol. 6, no. 2, pp. 126-140, 1994.
9. J. Bourjolly, G. Laporte, and H. Mercure, "A combinatorial column generation algorithm for the maximum clique and stable set problem," Technical Report G-94-33, Les Cahiers du GERD, July 1994.
10. M. Brockington and J.C. Culberson, "Camuflating independent sets in quasi-random graphs," in Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, D.S. Johnson and M.A. Trick (Eds.), Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 221-242, American Mathematical Society, 1996.
11. R. Carraghan and P.M. Pardalos, "An exact algorithm for the maximum clique problem," Operations Research Letters, vol. 9, pp. 375-382, 1990.
12. C. Friden, A. Hertz, and D. de Werra, "Stabulus: a technique for finding stable sets in large graphs with tabu search," Computing, vol. 42, pp. 35-45, 1989.
13. C. Friden, A. Hertz, and D. de Werra, "An exact algoritithm based on tabu search for finding a maximum independent set in graph," Computers Opns. Res., vol. 17, no. 5, pp. 375-382, 1990.
14. M.R. Garey and D.S. Johnson, Computer and Intractability: A Guide to the Theory of NP-Completeness, Freeman: New York, 1979.
15. M. Gendrau and P. Soriano, "Tabu search algorithms for the maximum clique problem," in Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, D.S. Johnson and M. A. Trick (Eds.), Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 221-242, American Mathematical Society, 1996.
16. L.E. Gibbons, D.W. Hearn, and P.M. Pardalos, "A continuous based heuristic for the maximum clique problem," in Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, D.S. Johnson and M. A. Trick (Eds.), Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 103-124, American Mathematical Society, 1996.
17. F. Glover, "Future paths for integer programming and links to artificial intelligence," Computers Opns. Res., vol. 13, pp. 533-549, 1986.
18. M.K. Goldberg and R.D. Rivenburgh, "Constructing cliques using restricted backtracking," in Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, D.S. Johnson and M.A. Trick (Eds.), Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 285-307, American Mathematical Society, 1996.
19. T. Grossman, "Applying the inn model to the max clique problem," in Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, D.S. Johnson and M.A. Trick (Eds.), Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 125-145, American Mathematical Society, 1996.
20. S. Homer and M. Peinado, "Experiments with polynomial-time clique approximation algorithms on very large graphs," in Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, D.S. Johnson and M.A. Trick (Eds.), Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 147-167, American Mathematical Society, 1996.
21. A. Jagota, L. Sanchis, and R. Ganesan, "Approximately solving maximum clique using neural network and related heuristic," in Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, D.S. Johnson and M.A. Trick (Eds.), Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 169-204, American Mathematical Society, 1996.
22. L. Lovász and M.D. Plummer, Matching Theory, North-Holland: Amsterdam, 1986.
23. C. Mannino and A. Sassano, "An exact algorithm for the maximum stable set problem," J. Computational Optimization and Applications, vol. 3, pp. 243-258, 1994.
24. C. Mannino and A. Sassano, "Edge projection and the maximum stable set problem," in Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, D.S. Johnson and M. A. Trick (Eds.), Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 205-219, American Mathematical Society, 1996.
25. G.L. Nemhauser and G. Sigismondi, "A strong cutting plane/branch-and-bound algorithm for node packing," J. Ops. Res. Soc., vol. 43, no. 5, pp. 443-457, 1992.
26. L. Orlandani, "Algoritmi di ricerca tabu per il problema del maxclique," Master's Thesis, Dipartimento di Matematica, Facoltà di Scienze Matematiche, Fisiche e Naturali, Via della Ricerca Scientifica, 00133 Rome, Italy, 1994.
27. P. Pardalos and J. Xue, "The maximum clique problem," J. of Global Optimization, vol. 4, no. 3, pp. 286-301, 1994.
28. E.C. Sewell, "A branch and bound algorithm for the stability number of a sparse graph," INFORMS J. on Comp., May 1995, to appear.
29. C. De Simone and A. Sassano, "Stability number of bull and chair-free graphs," Discrete Applied Mathematics, vol. 41, pp. 121-129, 1993.
30. Jue Xue, "Fast algorithms for the vertex packing problem," Ph.D. Thesis, Graduate School of Industrial Administration, Carnegie Mellon University, April 1991.