Combining graph structure exploitation and propositional reasoning for the maximum clique problem

Proceedings - International Conference on Tools with Artificial Intelligence, ICTAI

Volumn 1, Issue , 2010, Pages 344-351

  Li, Chu Min ^a   Quan, Zhe ^a  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

Branch and bound; Maxclique; MaxSAT

Indexed keywords

BRANCH AND BOUNDS; BRANCH-AND-BOUND ALGORITHMS; CARDINALITIES; GRAPH G; GRAPH STRUCTURES; INDEPENDENT SET; MAX-SAT; MAXCLIQUE; MAXIMUM CLIQUE; MAXIMUM CLIQUE PROBLEMS; RANDOM GRAPHS; STRUCTURAL INFORMATION; UPPER BOUND;

ALGORITHMS; BRANCH AND BOUND METHOD; GRAPHIC METHODS;

PROBLEM SOLVING;

EID: 78751476116     PISSN: 10823409     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICTAI.2010.57     Document Type: Conference Paper

References (21)

1. Carlos Ansótegui, María Luisa Bonet, and Jordi Levy. Solving (weighted) partial MaxSAT through satisfiability testing, In Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing, SAT-2009, Swansea, UK, pages 427-440. Springer LNCS 5584, 2009.
2. R. Carraghan, P. M. Pardalos, An exact algorithm for the maximum clique problem, Operations Research Letters, 9(6): 375-382 (1990).
3. M. Chudnovsky, N. Robertson, P. Seymour, R. Thomas, The strong perfect graph theorem. Annals of Mathematics 164 (1): 51-229, 2006
4. T. Fahle, Improving a branch-and-bound algorithm for maximum clique, Proceedings of ESA-2002, pp. 485-498, 2002.
5. Z. Fu, S. Malik, On solving the partial Max-sat problem, in proceedings of SAT 2006, LNCS 4121, pp 252-265, Springer, 2006
6. M. Grtschel, L. Lovsz, A. Schrijver, (1988), Geometric Algorithms and Combinatorial Optimization, Springer-Verlag. See especially chapter 9, "Stable Sets in Graphs", pp. 273-303
7. F. Heras, J. Larrosa, and A. Oliveras, An efficient weighted Max-SAT solver, Journal of Artificial Intelligence Research, 31:1-32, 2008.
8. J. Konc, D. Janezic, An improved branch and bound algorithm for the maximum clique problem, Communications in Mathematical and in Computer Chemistry, 58 (2007) pp. 569-590.
9. F. Heras, J. Larrosa, A Max-SAT Inference-Based Pre-processing for Max-Clique, in proceedings of SAT'2008, LNCS 4996, pp. 139-152, 2008.
10. C. M. Li and F. Manyà, Max-sat, hard and soft constraints. In A. Biere, H. van Maaren, and T. Walsh, editors, Handbook of Satisfiability, Pages 613-631, IOS Press, 2009.
11. C. M. Li, F. Manyà, and J. Planes, New inference rules for Max-SAT, Journal of Artificial Intelligence Research, 9(6): 375-382 (1990).
12. C. M. Li, F. Manyà, and Jordi. Planes, Detecting disjoint inconsistent subformulas for computing lower bounds for max-sat, Proceedings of AAAI'06, pages 86-91. AAAI Press, 2006.
13. C. M. Li, F. Manyà and J. Planes, Exploiting unit propagation to compute lower bounds in branch and bound MaxSAT solvers, proceedings of CP'05, LNCS 3709 Springer, 2005, pp 403-414.
14. C. M. Li, Zhe Quan, An Efficient Branch-and-Bound Algorithm based on MaxSAT for the Maximum Clique Problem, to appear in Proceedings of AAAI'2010, .
15. Vasco M. Manquinho, João P. Marques Silva, and Jordi Planes. Algorithms for weighted boolean optimization. In Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing, SAT-2009, Swansea, UK, pages 495-508. Springer LNCS 5584, 2009.
16. P. R. J. Ostergard, A fast algorithm for the maximum clique problem, Discrete Applied Mathematics, 120 (2002), 197-207.
17. P. R. J. Ostergard, The maximum clique problem, Journal of Global Optimization, 4: 301-328, 1994.
18. W. Pullan, H. H. Hoos, Dynamic Local Search for the Maximum Clique Problem, Journal of Artificial Intelligence Research, Vol. 25, pp. 159-185, 2006.
19. J.-C. Regin, Solving the maximum clique problem with constraint programming, Proceedings of CPAIOR'03, Springer, LNCS 2883, pp. 634-648, 2003.
20. E. Tomita, T. Kameda, An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments, J. Glob Optim, (2007) 37:95-111.
21. E. Tomita, T. Seki, An efficient branch-and-bound algorithm for finding a maximum clique, Discrete Mathematics and Theoretical Computer Science, LNCS 2731, pp. 278-289 (2003).