Abstract
We show how techniques from state-of-the-art branch and bound algorithms for the maximum clique problem can be adapted to solve the maximum balanced induced biclique problem. We introduce a simple and effective symmetry breaking technique. Finally, we discuss one particular class of graphs where the algorithm’s bound is ineffective, and show how to detect this situation and fall back to a simpler but faster algorithm. Computational results on a series of standard benchmark problems are included.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)
San Segundo, P., Rodríguez-Losada, D., Jiménez, A.: An exact bit-parallel algorithm for the maximum clique problem. Comput. Oper. Res. 38(2), 571–581 (2011)
San Segundo, P., Matia, F., Rodríguez-Losada, D., Hernando, M.: An improved bit parallel exact maximum clique algorithm. Optimization Letters (2011)
Crawford, J., Ginsberg, M., Luks, E., Roy, A.: Symmetry-breaking predicates for search problems. In: KR 1996: Principles of Knowledge Representation and Reasoning, pp. 148–159. Morgan Kaufmann (1996)
Gent, I.P., Petrie, K.E., François Puget, J.: Symmetry in constraint programming. In: Handbook of Constraint Programming, pp. 329–376. Elsevier (2006)
Gent, I.P., Harvey, W., Kelsey, T.: Groups and constraints: Symmetry breaking during search. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 415–430. Springer, Heidelberg (2002)
Backofen, R., Will, S.: Excluding symmetries in constraint-based search. Constraints 7(3-4), 333–349 (2002)
Tomita, E., Seki, T.: An efficient branch-and-bound algorithm for finding a maximum clique. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds.) DMTCS 2003. LNCS, vol. 2731, pp. 278–289. Springer, Heidelberg (2003), http://dx.doi.org/10.1007/3-540-45066-1_22
Tomita, E., Kameda, T.: An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments. Journal of Global Optimization 37(1), 95–111 (2007)
Tomita, E., Sutani, Y., Higashi, T., Takahashi, S., Wakatsuki, M.: A simple and faster branch-and-bound algorithm for finding a maximum clique. In: Rahman, M. S., Fujita, S. (eds.) WALCOM 2010. LNCS, vol. 5942, pp. 191–203. Springer, Heidelberg (2010)
Prosser, P.: Exact Algorithms for Maximum Clique: A Computational Study. Algorithms 5(4), 545–587 (2012)
Batsyn, M., Goldengorin, B., Maslov, E., Pardalos, P.M.: Improvements to MCS algorithm for the maximum clique problem. Journal of Combinatorial Optimization, 1–20 (2013)
McCreesh, C., Prosser, P.: Multi-threading a state-of-the-art maximum clique algorithm. Algorithms 6(4), 618–635 (2013)
Stark, C., Breitkreutz, B.J., Reguly, T., Boucher, L., Breitkreutz, A., Tyers, M.: Biogrid: A general repository for interaction datasets. Nucleic Acids Research 34(suppl. 1), D535–D539 (2006)
Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the really hard problems are. In: Proceedings of the 12th International Joint Conference on Artificial Intelligence, IJCAI 1991, vol. 1, pp. 331–337. Morgan Kaufmann Publishers Inc., San Francisco (1991)
Depolli, M., Konc, J., Rozman, K., Trobec, R., Janežič, D.: Exact parallel maximum clique algorithm for general and protein graphs. Journal of Chemical Information and Modeling 53(9), 2217–2228 (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
McCreesh, C., Prosser, P. (2014). An Exact Branch and Bound Algorithm with Symmetry Breaking for the Maximum Balanced Induced Biclique Problem. In: Simonis, H. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2014. Lecture Notes in Computer Science, vol 8451. Springer, Cham. https://doi.org/10.1007/978-3-319-07046-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-07046-9_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07045-2
Online ISBN: 978-3-319-07046-9
eBook Packages: Computer ScienceComputer Science (R0)