Complexity of Approximating Closest Substring Problems

  • Patricia A. Evans
  • Andrew D. Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2751)

Abstract

The closest substring problem, where a short string is sought that minimizes the number of mismatches between it and each of a given set of strings, is a minimization problem with a polynomial time approximation scheme [6]. In this paper, both this problem and its maximization complement, where instead the number of matches is maximized, are examined and bounds on their hardness of approximation are proved. Related problems differing only in their objective functions, seeking either to maximize the number of strings covered by the substring or maximize the length of the substring, are also examined and bounds on their approximability proved. For this last problem of length maximization, the approximation bound of 2 is proved to be tight by presenting a 2-approximation algorithm.

Keywords

Approximation algorithms Hardness of approximation Closest Substring 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arora, S.: Probabilistic checking of proofs and the hardness of approximation problems. PhD thesis, UC Berkeley (1994)Google Scholar
  2. 2.
    Lund, C., Yannakakis, M.: On the hardness of approximating minimization problems. Journal of the ACM 41(5) (1994)Google Scholar
  3. 3.
    Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In: Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 475–484 (1997)Google Scholar
  4. 4.
    Feige, U.: A threshold of log n for approximating set cover. Journal of the ACM 45(4), 634–652 (1998)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Lanctot, J.K., Li, M., Ma, B., Wang, S., Zhang, L.: Distinguishing string selection problems. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 633–642. ACM Press, New York (1999)Google Scholar
  6. 6.
    Li, M., Ma, B., Wang, L.: On the closest string and substring problems. Journal of the ACM 49(2), 157–171 (2002)CrossRefMathSciNetGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Sagot, M.-F.: Spelling approximate repeated or common motifs using a suffix tree. In: Lucchesi, C.L., Moura, A.V. (eds.) LATIN 1998. LNCS, vol. 1380, p. 374. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Patricia A. Evans
    • 1
  • Andrew D. Smith
    • 1
    • 2
  1. 1.University of New BrunswickFredericton N.B.Canada
  2. 2.Ontario Cancer InstituteUniversity Health Network, Suite 703TorontoCanada

Personalised recommendations