LATA 2011: Language and Automata Theory and Applications pp 336-341 | Cite as
Unique Small Subgraphs Are Not Easier to Find
Conference paper
Abstract
Given a pattern graph H of fixed size, and a host graph G guaranteed to contain at most one occurrence of a subgraph isomorphic to H, we show that both the problem of finding such an occurrence (if any) as well as the decision version of the problem are as hard as in the general case when G may contain several occurrences of H.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Alon, N., Dao, P., Hajirasouliha, I., Hormozdiari, F., Sahinalp, S.: Biomolecular network motif counting and discovery by color coding. In: Proceedings 16th International Conference on Intelligent Systems for Molecular Biology (ISMB), Toronto, Canada, July 19-23, pp. 241–249 (2008)Google Scholar
- 2.Alon, N., Naor, M.: Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions. Algorithmica 16(4), 434–449 (1996)MathSciNetCrossRefMATHGoogle Scholar
- 3.Alon, N., Yuster, R., Zwick, U.: Color-coding. Journal of the ACM 42(4), 844–856 (1995)MathSciNetCrossRefMATHGoogle Scholar
- 4.Alon, N., Yuster, R., Zwick, U.: Finding and counting given length cycles. Algorithmica 17(3), 209–223 (1997)MathSciNetCrossRefMATHGoogle Scholar
- 5.Bachman, P., Liu, Y.: Structure discovery in PPI networks using pattern-based network decomposition. Bioinformatics 25(14), 1814–1821 (2009)CrossRefGoogle Scholar
- 6.Chiba, N., Nishizeki, T.: Arboricity and subgraph listing algorithms. SIAM J. Comput. 14(1), 210–223 (1985)MathSciNetCrossRefMATHGoogle Scholar
- 7.Eisenbrand, F., Grandoni, F.: On the complexity of fixed parameter clique and dominating set. Theoretical Computer Science 326(1-3), 57–67 (2004)MathSciNetCrossRefMATHGoogle Scholar
- 8.Eppstein, D.: Subgraph isomorphism in planar graphs and related problems. J. Graph Algorithms Appl. 3(3), 1–27 (1999)MathSciNetCrossRefMATHGoogle Scholar
- 9.Gabow, H., Kaplan, H., Tarjan, R.: Unique maximum matching algorithms. J. Algorithms 40(2), 159–183 (2001)MathSciNetCrossRefMATHGoogle Scholar
- 10.Garey, M., Johnson, D.: Computers and intractability. A guide to the theory of NP-completeness. A Series of Books in the Mathematical Sciences. WH Freeman and Company, New York (2003)MATHGoogle Scholar
- 11.Huang, X., Pan, V.: Fast rectangular matrix multiplications and applications. Journal of Complexity 14, 257–299 (1998)MathSciNetCrossRefMATHGoogle Scholar
- 12.Itai, A., Rodeh, M.: Finding a Minimum Circuit in a Graph. SIAM Journal on Computing 7, 413–423 (1978)MathSciNetCrossRefMATHGoogle Scholar
- 13.Kloks, T., Kratsch, D., Muller, H.: Finding and counting small induced subgraphs efficiently. Information Processing Letters 74(3), 115–121 (2000)MathSciNetCrossRefMATHGoogle Scholar
- 14.Kowaluk, M., Lingas, A.: Unique lowest common ancestors in dags are almost as easy as matrix multiplication. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 265–274. Springer, Heidelberg (2007)CrossRefGoogle Scholar
- 15.Kowaluk, M., Lingas, A., Lundell, E.: Counting and detecting small subgraphs via equations and matrix multiplication. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1468–1476 (2011)Google Scholar
- 16.Nešetřil, J., Poljak, S.: On the complexity of the subgraph problem. Commentationes Mathematicae Universitatis Carolinae 26(2), 415–419 (1985)MathSciNetMATHGoogle Scholar
- 17.Plehn, J., Voigt, B.: Finding minimally weighted subgraphs. In: Graph-Theoretic Concepts in Computer Science (WG), pp. 18–29 (1991)Google Scholar
- 18.Seidel, R.: On the all-pairs-shortest-path problem. In: Proceedings of the Twenty-fourth Annual ACM Symposium on Theory of Computing (STOC), pp. 745–749 (1992)Google Scholar
- 19.Valiant, V., et al.: NP is as easy as detecting unique solutions. Theoretical Computer Science 47, 85–93 (1986)MathSciNetCrossRefMATHGoogle Scholar
- 20.Vassilevska, V., Williams, R.: Finding, minimizing, and counting weighted subgraphs. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing (STOC), pp. 455–464 (2009)Google Scholar
- 21.Wolinski, C., Kuchcinski, K., Raffin, E.: Automatic design of application-specific reconfigurable processor extensions with UPaK synthesis kernel. ACM Transactions on Design Automation of Electronic Systems (TODAES) 15(1), 1–36 (2009)CrossRefGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2011