Abstract
The longest common subsequence problem (LCS) and the closest substring problem (CSP) are two models for the finding of common patterns in strings. The two problem have been studied extensively. The former was previously proved to be not polynomial-time approximable within ratio n δ for a constant δ. The latter was previously proved to be NP-hard and have a PTAS. In this paper, the longest common rigid subsequence problem (LCRS) is studied. LCRS shares similarity with LCS and CSP and has an important application in motif finding in biological sequences. LCRS is proved to be Max-SNP hard in this paper. An exact algorithm with quasi-polynomial average running time is also provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Identification of a src sh3 domain binding motif by screening a random phage display library. Journal of Biological Chemistry 269, 24034–24039 (1994)
Adebiyi, E.F., Kaufmann, M.: Extracting common motifs under the levenshtein measure: theory and experimentation. In: Guigó, R., Gusfield, D. (eds.) WABI 2002. LNCS, vol. 2452, pp. 140–156. Springer, Heidelberg (2002)
Jiang, T., Li, M.: On the approximation of shortest common supersequence and longest common subsequences. SIAM Journal on Computing 24(5), 1122–1139 (1995)
Keich, U., Pevzner, P.A.: Finding motifs in the twilight zone. In: Proceedings of the sixth annual international conference on computational biology, pp. 195–204 (2002)
Kevin Lanctot, J., Li, M., Ma, B., Wang, S., Zhang, L.: Distinguishing string selection problems. Information and Computation 185(1), 41–55 (2003); Early version appeared in SODA 1999
Li, M., Ma, B., Wang, L.: Finding Similar Regions in Many Strings. In: Proceedings of the thirty-first annual ACM symposium on Theory of computing (STOC), Atlanta, May 1999, pp. 473–482 (1999)
Li, M., Ma, B., Wang, L.: Finding Similar Regions in Many Sequences. Journal of Computer and System Sciences 65(1), 73–96 (2002); Early version appeared in STOC 1999
Li, M., Ma, B., Wang, L.: On the Closest String and Substring Problems. Journal of the ACM 49(2), 157–171 (2002); Early versions appeared in STOC 1999 and CPM 2000
Ma, B.: A Polynomial Time Approximation Scheme for the Closest Substring Problem. In: Giancarlo, R., Sankoff, D. (eds.) CPM 2000. LNCS, vol. 1848, pp. 99–107. Springer, Heidelberg (2000)
Maier, D.: The complexity of some problems on subsequences and supersequences. Journal of the ACM 25, 322–336 (1978)
Waterman, M.S., Arratia, R., Galas, D.J.: Pattern recognition in several sequences: consensus and alignment. Bulletin of Mathematical Biology 46(4), 515–527 (1984)
Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. Journal of Computer and System Sciences 43, 425–440
Rajasekaran, S., Balla, S., Huang, C.: Exact algorithms for planted motif challenge problems. In: Proceedings of the 3rd Asia Pacific Bioinformatics Conference (2005)
Rajasekaran, S., Balla, S., Huang, C.-H., Thapar, V., Gryk, M., Maciejewski, M., Schiller, M.: Exact algorithms for motif search. In: Proceedings of the 3rd Asia Pacific Bioinformatics Conference (2005)
Rigoutsos, I., Floratos, A.: Combinatorial pattern discovery in biological sequences: the teiresias algorithm. Bioinformatics 14(1), 55–67 (1998)
Stormo, G., Hartzell III., G.W.: Identifying protein-binding sites from unaligned dna fragments. Proc. Natl. Acad. Sci. USA 88, 5699–5703 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ma, B., Zhang, K. (2005). On the Longest Common Rigid Subsequence Problem. In: Apostolico, A., Crochemore, M., Park, K. (eds) Combinatorial Pattern Matching. CPM 2005. Lecture Notes in Computer Science, vol 3537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496656_2
Download citation
DOI: https://doi.org/10.1007/11496656_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26201-5
Online ISBN: 978-3-540-31562-9
eBook Packages: Computer ScienceComputer Science (R0)