Advertisement

Approximations and Partial Solutions for the Consensus Sequence Problem

  • Amihood Amir
  • Haim Paryenty
  • Liam Roditty
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7024)

Abstract

The problem of finding the consensus of a given set of strings is formally defined as follows: given a set of strings S = {s 1,…s k }, and a constant d, find, if it exists, a string s *, such that the Hamming distance of s * from each of the strings does not exceed d.

In this paper we study an LP relaxation for the problem. We prove an additive upper bound, depending only in the number of strings k, and randomized bounds. We show that empirical results are much better. We also compare our program with some algorithms reported in the literature, and it is shown to perform well.

Keywords

Consensus Sequence Integer Linear Program Close String Integral Solution Linear Programming Relaxation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ben-Dor, A., Lancia, G., Perone, J., Ravi, R.: Banishing bias from consensus sequences. In: Proceedings of the 8th Symposium on Combinatorial Pattern Matching, pp. 247–261 (1997)Google Scholar
  2. 2.
    Boucher, C., Brown, D.G., Durocher, S.: On the structure of small motif recognition instances. In: Amir, A., Turpin, A., Moffat, A. (eds.) SPIRE 2008. LNCS, vol. 5280, pp. 269–281. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Gasieniec, L., Jansson, J., Lingas, A.: Efficient approximation algorithms for the Hamming center problem. In: Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, pp. 905–906 (1999)Google Scholar
  4. 4.
    Gasieniec, L., Jansson, J., Lingas, A.: Approximation algorithms for Hamming clustering problems 2, 289–301 (2004)Google Scholar
  5. 5.
    Gramm, J., Niedermeier, R., Rossmanith, P.: Exact solutions for closest string and related problems. In: Proceedings of the 12th International Symposium on Algorithms and Computation, pp. 441–453 (2001)Google Scholar
  6. 6.
    Gramm, J., Niedermeier, R., Rossmanith, P.: Fixed-parameter algorithms for closest string and related problems. Algorithmica 37(1), 25–42 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Stojanovic, N., Berman, P., Gumucio, D., Hardison, R., Miller, W.: A linear-time algorithm for the 1-mismatch problem. In: Rau-Chaplin, A., Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 1997. LNCS, vol. 1272, pp. 126–135. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  8. 8.
    Sze, S.-H., Lu, S., Chen, J.: Integrating sample-driven and pattern-driven approaches in motif finding. In: Jonassen, I., Kim, J. (eds.) WABI 2004. LNCS (LNBI), vol. 3240, pp. 438–449. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Lanctot, K., Li, M., Ma, B., Wang, S., Zhang, L.: Distinguishing string selec- tion problems. In: Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, pp. 633–642 (1999)Google Scholar
  10. 10.
    Li, M., Ma, B., Wang, L.: Finding similar regions in many strings. In: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pp. 473–482 (1999)Google Scholar
  11. 11.
    Li, M., Ma, B., Wang, L.: On the closest string and substring problems. Journal of the ACM 49(2), 157–171 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Ma, B., Sun, X.: More efficient algorithms for closest string and substring problems. In: Vingron, M., Wong, L. (eds.) RECOMB 2008. LNCS (LNBI), vol. 4955, pp. 396–409. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Chimani, M., Woste, M., Bocker, S.: A Closer Look at the Closest String and Closest Substring Problem, pp. 13–24. ALENEX (2011)Google Scholar
  14. 14.
    Hufsky, F., Kuchenbecker, L., Jahn, K., Stoye, J., Böcker, S.: Swiftly computing center strings. In: Moulton, V., Singh, M. (eds.) WABI 2010. LNCS, vol. 6293, pp. 325–336. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Lenstra, H.W.: Integer programming with a fixed number of variables. Mathematics of Operations Research 8, 538–548 (1983)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Amihood Amir
    • 1
    • 2
  • Haim Paryenty
    • 1
  • Liam Roditty
    • 1
  1. 1.Department of Computer ScienceBar Ilan UniversityRamat GanIsrael
  2. 2.Department of Computer ScienceJohns Hopkins UniversityBaltimoreUSA

Personalised recommendations