Erratum: An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments (Journal of Global Optimization (2007) 37 (95-111) DOI: 10.1007/s10898-006-9039-7);An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments

Journal of Global Optimization

Volumn 37, Issue 1, 2007, Pages 95-111

  Tomita, Etsuji ^a   Kameda, Toshikatsu ^a  

^a UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

Author keywords

Algorithm; Approximate coloring; Branch and bound; Computational experiments; Maximum clique

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; DNA SEQUENCES; GRAPHIC METHODS; IMAGE ANALYSIS; SORTING;

BIOINFORMATICS; BIOMOLECULAR COMPUTATION; COMPUTATIONAL EXPERIMENTS; QUANTUM CIRCUITS;

ALGORITHMS;

EID: 33845292891     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-008-9362-2     Document Type: Erratum

References (30)

1. Akutsu, T., Hayashida, M., Bahadur, D.K.C., Tonika, E., Suzuki, J., Horimoto, K.: Dynamic programming and clique based approaches for protein threading with profiles and constraints, IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences E89-A 1215-1222 (2006)
2. : The preliminary version was presented in: Akutsu, T., Hayashida, M., Tomita, E., Suzuki, J., Horimoto, K.: Protein threading with profiles and constraints, Proc. IEEE Symposium on Bioinformatics and Bioengineering (BIBE 2004). pp. 537-544 (2004 )
3. Bahadur, D.K.C., Akutsu, T., Tomita, E., Seki, T., Fujiyama, A.: Point matching under non-uniform distortions and protein side chain packing based on efficient maximum clique algorithms. Genome Inform. 13, 143-152 (2002)
4. Bahadur, D.K.C., Tomita, E., Suzuki, J., Horimoto, K., Akutsu, T.: Protein side-chain packing problem: a maximum edge-weight clique algorithmic approach, J. Bioinform Comput. Biol. 3, 103-126 (2005)
5. Bahadur, D.K.C., Tomita, E., Suzuki, J., Horimoto, K., Akutsu, T.: Protein threading with profiles and distance constraints using clique based algorithms. J. Bioinform. Comput. Biol. 4, 19-42 (2006)
6. Balas, E., Yu, C.S.: Finding a maximum clique in an arbitrary graph. SIAM J. Comput. 15, 1054-1068 (1986)
7. Balas, E., Ceria, S., Cornuéjols, G., Pataki, G.: Polyhedral methods for the maximum clique problem, In: Johnson and Trick (eds.) pp. 11-28 (1996)
8. 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, Supplement Vol. A, pp. 1-74. Kluwer Academic Publishers, Dordrecht (1999)
9. Bourjolly, J.-M., Gill, P., Laporte, G., Mercure, H.: An exact quadratic 0-1 algorithm for the stable set problem, In: Johnson and Trick (eds.) pp. 53-73 (1996)
10. Carraghan, R., Pardalos, P.M.: An exact algorithm for the maximum clique problem. Oper. Res. Lett. 9, 375-382 (1990)
11. Corno, F., Prinetto, P., Sonza Reorda, M.: Using symbolic techniques to find the maximum clique in very large sparse graphs. Proc. European Design and Test Conference(EDTC 1995). pp. 320-324 (1995)
12. Fahle, T.: Simple and fast: Improving a branch-and-bound algorithm for maximum clique. European Symposium on Algorithms 2002, LNCS 2461. pp. 485-498 (2002)
13. Fujii, T., Tomita, E.: On efficient algorithms for finding a maximum clique. Technical Report of IECE, AL81-113. pp. 25-34 (1982)
14. Hotta, K., Tomita, E., Takahashi, H.: A view-invariant human face detection method based on maximum cliques. Trans. IPSJ, 44, SIG14(TOM9), 57-70 (2003)
15. Johnson, D.S., Trick, M.A. (eds.): Cliques, coloring, and satisfiability. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26. American Mathematical Society Providence, RI (1996)
16. Kobayashi, S., Kondo, T., Okuda, K., Tomita, E.: (2003), Extracting globally structure free sequences by local structure freeness, In: Chen, J., Reif, J. (eds.): Proc. Ninth International Meeting on DNA Based Computers, p. 206 (2003)
17. Nakui, Y., Nishino, T., Tomita, E., Nakamura, T.: On the minimization of the quantum circuit depth based on a maximum clique with maximum vertex weight. Technical Report of RIMS, 1325, pp. 45-50. Kyoto University (2003)
18. Östergård, P.R.J.: A fast algorithm for the maximum clique problem. Discrete Appl. Math. 120, 197-207 (2002)
19. Pardalos, P.M., Xue J.: The maximum clique problem. J. Global Optim. 4, 301-328 (1994)
20. Robson, J.M.: Algorithms for maximum independent sets. J. Algorithm, 7, 425-440 (1986)
21. Sewell, E.G.: A branch and bound algorithm for the stability number of a sparse graph. INFORMS J. Comput. 10, 438-447 (1998)
22. Stix, V.: Target-oriented branch and bound method for global optimization. J. Global Optim. 26, 261-277 (2003)
23. Tarjan, R.E., Trojanowski, A.E.: Finding a maximum independent set. SIAM J. Comput. 6, 537-546 (1977)
24. Tomita, E., Yamada, M.: An algorithm for finding a maximum complete subgraph. Conference Records of IECE (Technical Report of the National Convention of IECE 1978), p. 8 (1978)
25. Tomita, E., Kohata, Y., Takahashi, H.: A simple algorithm for finding a maximum clique. Technical Report of the University of Electro-Communications, UEC-TR-CS(1) (1988)
26. Tomita, E., Seki, T.: An efficient branch-and-bound algorithm for finding a maximum clique. Proc. Discrete Mathematics and Theoretical Computer Science. LNCS 2731, pp. 278-289 (2003)
27. Tomita, E., Kameda, T.: (revised 2006), An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments. Technical Report of the University of Electro-Communications, UEC-TR-CAS10-2005 (2005)
28. Tomita, E., Nakagawa, T., Urabe, S.: An experimental comparison of algorithms for finding a maximum clique. Technical Report of The University of Electro-Communications, UEC-TR-CAS3-2006 (2006)
29. Tomita, E., Tanaka, A., Takahashi, H.: (to appear), The worst-case time complexity for generating all maximal cliques and computational experiments, Theoretical Computer Science (An invited paper in the Special Issue on COCOON 2004). The preliminary version was presented in: Tomita, E., Tanaka, A., Takahashi, H., The worst-case time complexity for generating all maximal cliques. Proc. International Computing and Combinatorics Conference (COCOON 2004), LNCS 3106. pp. 278-289.
30. Wood, D. R.: An algorithm for finding a maximum clique in a graph. Operations Res. Lett. 21, 211-217 (1977)