Polynomial-time algorithms for computing characteristic strings

  • Minoru Ito
  • Kuniyasu Shimizu
  • Michio Nakanishi
  • Akihiro Hashimoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 807)


The difference between two strings is the minimum number of editing steps (insertions, deletions, changes) that convert one string into the other. Let S be a finite set of strings, let T be a subset of S, and let δ be a positive integer. A δ-characteristic string of T under S is a string that is a common substring of T and that has at least δ-differences from any substring of any string in S − T. In this paper, the following result is presented.lt can be decided in O(∥T∥+l2 · ¦S− T¦+l ·δ·¦¦S−T¦¦) time whether or not there exists a δ-characteristic string of T under S, where l denotes the length of a shortest string in T, ¦S− T¦ the cardinality of S − T, and ∥T∥ the size of T. If such a string exits, then all the shortest δ-characteristic strings of T under S can also be obtained in that time.


characteristic string approximate pattern matching DNA probe 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.S.Boyer and J.S.Moore: “A fast string searching algorithm,” Comm. ACM, 20, 10, pp.762–772 (Oct. 1977).Google Scholar
  2. 2.
    R.Dular, R.Kajioka and S.Kasatiya: “Comparison of Gene-Probe Commercial Kit and Culture Technique for the Diagnosis of Mycoplasma pneumoniae Infection,” Journal of Clinical Microbiology, 26, 5, pp.1068–1069 (May 1988).Google Scholar
  3. 3.
    M.Hasidume, M.Ito, M.Nakanishi and A.Hashimoto: “A linear-time algorithm for computing a shortest characteristic substring of strings” (in Japanese), IEICE Technical Report, COMP93-36, pp.39–46 (July 1993).Google Scholar
  4. 4.
    D.G.Higgins and P.M.Sharp: “Fast and sensitive multiple sequence alignments on a microcomputer,” CABIOS, 5, 2, pp.151–153 (Apr. 1989).Google Scholar
  5. 5.
    D.E.Knuth, J.H.Morris and V.R. Pratt: “Fast pattern matching in strings,” SIAM Journal on Computing, 6, 2, pp.323–350 (June 1977).Google Scholar
  6. 6.
    G.M.Landau and U.Vishkin: “Introducing efficient parallelism into approximate string matching and a new serial algorithm,” Proc. 18th ACM Symp. on Theory of Computing, pp.220–230 (May 1986).Google Scholar
  7. 7.
    G.M.Landau and U.Vishkin: “Fast parallel and serial approximate string matching,” Journal of Algorithms, 10, pp.157–169 (June 1989).Google Scholar
  8. 8.
    A.J.L.Macario and E.C.de Macario: “Gene Probes for Bacteria,” Academic Press (1990)Google Scholar
  9. 9.
    M.Nasu, K.Shimada, S.Inaoka, K.Tani and M.Kondo: “ Natural bacterial populations in river water determined by 16S and 23S rRNA-targeted oligonucleotide probes,” (submitted to Biomédical and Environmental Sciences).Google Scholar
  10. 10.
    W.R.Pearson and D.J.Lipman: “Improved tools for biological sequence comparison,” Proc. Natl. Acad. Sci. USA, 85, pp.2444–2448 (Apr. 1988).Google Scholar
  11. 11.
    P.H.Sellers: “The theory and computation of evolutionary distances: Pattern recognition,” Journal of Algorithms, 1, pp.359–373 (Dec. 1980).Google Scholar
  12. 12.
    E.Ukkonen: “On approximate string matching,” Lecture Notes in Computer Science, 158, pp.487–495 (Aug. 1983).Google Scholar
  13. 13.
    E.Ukkonen: “Finding approximate patterns in strings,” Journal of Algorithms, 6, 1, pp.132–137 (Mar. 1985).Google Scholar
  14. 14.
    E.Ukkonen: “Algorithms for approximate string matching,” Information and Control, 64, pp.100–118 (Mar. 1985).Google Scholar
  15. 15.
    P.Weiner: “Linear pattern matching algorithms,” Proc. IEEE 14th Symposium on Switching and Automata Theory, pp.1–11 (1973)Google Scholar
  16. 16.
    ”Genome Databases,” Science, 254 (Oct. 1991).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Minoru Ito
    • 1
  • Kuniyasu Shimizu
    • 2
  • Michio Nakanishi
    • 3
  • Akihiro Hashimoto
    • 3
  1. 1.Graduate School of Information ScienceNara Institute of Science and TechnologyNaraJapan
  2. 2.Information Systems Engineering LaboratoryTOSHIBA CorporationTokyoJapan
  3. 3.Department of Information and Computer Sciences, Faculty of Engineering ScienceOsaka UniversityOsakaJapan

Personalised recommendations