The worst-case time complexity for generating all maximal cliques and computational experiments

Theoretical Computer Science

Volumn 363, Issue 1, 2006, Pages 28-42

  Tomita, Etsuji ^a   Tanaka, Akira ^a,b   Takahashi, Haruhisa ^a  

^a UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

^b Toyota Techno Service Corporation   (Japan)

Author keywords

Computational experiments; Enumeration; Maximal cliques; Worst case time complexity

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; FUNCTION EVALUATION;

COMPUTATIONAL EXPERIMENTS; ENUMERATION; MAXIMAL CLIQUES; WORST CASE TIME COMPLEXITY;

GRAPH THEORY;

EID: 33749264452     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2006.06.015     Document Type: Article

References (29)

1. T. Akutsu, M. Hayashida, E. Tomita, J. Suzuki, K. Horimoto, Protein threading with profiles and constraints, Proc. IEEE Symp. Bioinform. Bioeng. (2004) 537-544;
2. T. Akutsu, M. Hayashida, D.K.C. Bahadur, E. Tomita, J. Suzuki, K. Horimoto, Dynamic programming and clique based approaches for protein threading with profiles and constraints, IEICE Trans. Fund. Electron. Commun. Comput. Sci. E89-A (2006) 1215-1222.
3. Bahadur D.K.C., Akutsu T., Tomita E., Seki T., and Fujiyama A. Point matching under non-uniform distortions and protein side chain packing based on efficient maximum clique algorithms. Genome Inform. 13 (2002) 143-152
4. Bahadur D.K.C., Tomita E., Suzuki J., and Akutsu T. Protein side-chain packing problem: a maximum edge-weight clique algorithmic approach. J. Bioinform. Comput. Biol. 3 (2005) 103-126
5. Bahadur D.K.C., Tomita E., Suzuki J., Horimoto K., and Akutsu T. Protein threading with profiles and distance constraints using clique based algorithms. J. Bioinform. Comput. Biol. 4 (2006) 19-42
6. I.M. Bomze, M. Budinich, P.M. Pardalos, M. Pelillo, The maximum clique problem, in: D.-Z. Du, P.M. Pardalos (Eds.), Handbook of Combinatorial Optimization, Supplement Vol. A, Kluwer Academic Publishers, Dordrecht, 1999, pp. 1-74.
7. Bron C., and Kerbosch J. Algorithm 457, finding all cliques of an undirected graph. Comm. ACM 16 (1973) 575-577
8. Chiba N., and Nishizeki T. Arboricity and subgraph listing algorithms. SIAM J. Comput. 14 (1985) 210-223
9. Hattori M., Okuno Y., Goto S., and Kanehisa M. Development of a chemical structure comparison method for integrated analysis of chemical and genomic information in the metabolic pathways. J. Amer. Chem. Soc. 125 (2003) 11853-11865
10. Johnston H.C. Cliques of a graph-variations on the Bron-Kerbosch algorithm. Int. J. Comput. Inform. Sci. 5 (1976) 209-238
11. D.S. Johnson, M.A. Trick (Eds.), Cliques, Coloring, and Satisfiability, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 26, American Mathematical Society, Providence, RI, 1996.
12. Kobayashi S., Kondo T., Okuda K., and Tomita E. Extracting globally structure free sequences by local structure freeness. Proc. DNA 9 (2003) 206
13. Koch I. Enumerating all connected maximal common subgraphs in two graphs. Theoret. Comput. Sci. 250 (2001) 1-30
14. Lawler E.L., Lenstra J.K., and Rinnooy Kan A.H.G. Generating all maximal independent sets: NP-hardness and polynomial-time algorithms. SIAM J. Comput. 9 (1980) 558-565
15. K. Makino, T. Uno, New algorithms for enumerating all maximal cliques, SWAT 2004, Lecture Notes in Computer Science, Vol. 3111, 2004, pp. 260-272.
16. Mohseni-Zadeh S., Brézellec P., and Risler J.-L. Cluster-C, an algorithm for the large-scale clustering of protein sequences based on the extraction of maximal cliques. Comput. Biol. Chem. 28 (2004) 211-218
17. Mohseni-Zadeh S., Louis A., Brézellec P., and Risler J.-L. PHYTOPROT: a database of clusters of plant proteins. Nucleic Acids Res. 32 (2004) D351-D353
18. Moon J.W., and Moser L. On cliques in graphs. Israel J. Math. 3 (1965) 23-28
19. T. Nakagawa, E. Tomita, Experimental comparisons of algorithms for generating all maximal cliques, Technical Report of IPSJ, 2004-MPS-52, 2004, pp. 41-44.
20. Pardalos P.M., and Xue J. The maximum clique problem. J. Global Optim. 4 (1994) 301-328
21. Robson J.M. Algorithms for maximum independent sets. J. Algorithms 7 (1986) 425-440
22. Tarjan R.E., and Trojanowski A.E. Finding a maximum independent set. SIAM J. Comput. 6 (1977) 537-546
23. E. Tomita, T. Seki, An efficient branch-and-bound algorithm for finding a maximum clique, DMTCS 2003, Lecture Notes in Computer Science, Vol. 2731, 2003, pp. 278-289;
24. E. Tomita, T. Kameda, An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments, J. Global Optim. (2006), in press;
25. Y. Sutani, E. Tomita, Computational experiments and analyses of a more efficient algorithm for finding a maximum clique, Technical Report of IPSJ, 2005-MPS-57, 2005, pp. 45-48, and others.
26. E. Tomita, A. Tanaka, H. Takahashi, The worst-case time complexity for finding all the cliques, Technical Report of the University of Electro-Communications, UEC-TR-C5(2), 1988.
27. E. Tomita, A. Tanaka, H. Takahashi, An optimal algorithm for finding all the cliques, Technical Report of IPSJ, 1989-AL-12, 1989, pp. 91-98.
28. E. Tomita, A. Tanaka, H. Takahashi, The worst-case time complexity for generating all maximal cliques, COCOON 2004, Lecture Notes in Computer Science, Vol. 3106, 2004, pp. 161-170.
29. Tsukiyama S., Ide M., Ariyoshi H., and Shirakawa I. A new algorithm for generating all the maximal independent sets. SIAM J. Comput. 6 (1977) 505-517