, Volume 25, Issue 5, pp 565–580 | Cite as

Complexity of common subsequence and supersequence problems and related problems

  • V. G. Timkovskii


The article examines polynomial-time and intractable longest common subsequence and subword problems and shortest common supersequence and superword problems, both old and new. The results provide a more complete complexity characterization of these problems. Some applications are discussed, as well as the dual problems of common nonsubwords, nonsuperwords, nonsubsequences, and nonsupersequences.


Operating System Artificial Intelligence System Theory Related Problem Dual Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    M. R. Garey and D. S. Johnson, Computers and Intractability, Freeman, San Francisco (1979).Google Scholar
  2. 2.
    A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass. (1974).Google Scholar
  3. 3.
    M. L. Fredman, “On computing the length of the longest increasing subsequences,” Discr. Math.,11, No. 1, 29–36 (1975).Google Scholar
  4. 4.
    M. O. Dayhoff, “Computer aids to protein sequence determination,” J. Theor. Biol.,8, No. 1, 97–112 (1965).Google Scholar
  5. 5.
    M. O. Dayhoff, “Computer analysis of protein evolution,” Sci. Am.,221, No. 1, 86–95 (1969).Google Scholar
  6. 6.
    S. B. Needleman and C. S. Wunsch, “A general method applicable to the search for similarities in the amino acid sequence of two proteins,” J. Molec. Biol.,48, 443–453 (1970).Google Scholar
  7. 7.
    D. Sunkoff and R. J. Cedergren, “A test for nucleotide sequence homology,” J. Molec. Biol.,77, 159–164 (1973).Google Scholar
  8. 8.
    R. A. Wagner and M. J. Fischer, “The string-to-string correction problem,” J. ACM,21, No. 1, 168–173 (1974).Google Scholar
  9. 9.
    R. Lowrance and R. W. Wagner, “An extension of the string-to-string correction problem,” J. ACM,22, No. 2, 177–183 (1975).Google Scholar
  10. 10.
    M. Rodeh, V. R. Pratt, and S. Even, “Linear algorithm for data compression via string matching,” J. ACM,28, No. 1, 16–27 (1981).Google Scholar
  11. 11.
    S. Y. Lu and K. S. Fu, “A sentence-to-sentence clustering procedure for pattern analysis,” IEEE Trans. Syst. Man, Cybern., SMC-8, 381–389 (1978).Google Scholar
  12. 12.
    N. M. Kapustin, Development of Technological Parts Machining Processes by Computer [in Russian], Mashinostroenie, Moscow (1976).Google Scholar
  13. 13.
    K. Tempelhof and H. Lichtenberg, “Technological standardization as a prerequisite for computer-aided design of technological processes,” in: N. M. Kapustin (ed.), Computer-Aided Design of Technological Processes [in Russian], Mashinostroenie, Moscow (1985), pp. 109–153.Google Scholar
  14. 14.
    A. M. Basin, V. N. Balabolin, V. V. Kryukov, et al., “An interactive system for multilevel design of technological processes of flexible production,” Vestn. Mashinostr., No. 2, 42–44 (1987).Google Scholar
  15. 15.
    P. H. Sellers, “An algorithm for the distance between two finite sequences,” J. Combin. Theory,16, 253–258 (1974).Google Scholar
  16. 16.
    D. S. Hirschberg, “A linear space algorithm for computing maximal sequences,” Commun. ACM,18, No. 6, 341–343 (1975).Google Scholar
  17. 17.
    D. S. Hirschberg, “Algorithms for longest common subsequence problem,” J. ACM,24, No. 4, 664–675 (1977).Google Scholar
  18. 18.
    J. W. Hunt and T. G. Szymanski, “A fast algorithm for computing longest common subsequences,” Commun. ACM,20, No. 5, 350–353 (1977).Google Scholar
  19. 19.
    W. J. Masek and M. S. Paterson, “A faster algorithm computing string edit distance,” J. Comput. Syst., Sci.,20, 18–31 (1980).Google Scholar
  20. 20.
    N. Nakatsu, Y. Kambayashi, and S. Yajima, “A longest common subsequence algorithm suitable for similar text strings,” Acta Inf.,18, 171–179 (1982).Google Scholar
  21. 21.
    A. Mukhopadhyay, “A fast algorithm for longest-common-subsequence problem,” Inform. Sci.,20, 69–82 (1980)Google Scholar
  22. 22.
    C. K. Wong and A. K. Chandra, “Bounds for the string editing problem,” J. ACM,23, No. 1, 13–16 (1976).Google Scholar
  23. 23.
    L. Allison and T. I. Dix, “A bit-string longest-common-subsequence algorithm,” Inform. Process. Lett.,23, 305–310 (1986).Google Scholar
  24. 24.
    C. B. Yang and R. C. T. Lee, “The mapping of 2-D array processors to 1-D array processors,” Parallel Comput.,3, 217–229 (1986).Google Scholar
  25. 25.
    W. J. Hsu and M. W. Du, “New algorithms for LCS problem,” J. Comput. Syst. Sci.,29, No. 2, 133–152 (1984).Google Scholar
  26. 26.
    S. K. Kumar and C. P. Rangan, “A linear space algorithm for the LCS problem,” Acta Inf.,24, 353–362 (1987).Google Scholar
  27. 27.
    A. V. Aho, D. S. Hirschberg, and J. D. Ullman, “Bounds on the complexity of the longest common subsequence problem,” J. ACM,23, No. 1, 1–12 (1976).Google Scholar
  28. 28.
    D. Maier, “The complexity of some problems on subsequences and supersequences,” J. ACM,25, No. 2, 322–336 (1978).Google Scholar
  29. 29.
    Yu. V. Matiyasevich, “On real-time recognition of the inclusion relation,” Zap. Nauch. Sem. LOMI AN SSSR,20, 104–114 (1971).Google Scholar
  30. 30.
    P. Weiner, “Linear pattern matching algorithms,” IEEE 14th Ann. Symp. on Switching and Automata Theory (1973), pp. 1–11.Google Scholar
  31. 31.
    E. M. McCreight, “space-economical suffix tree construction algorithm,” J. ACM,23, 262–272 (1976).Google Scholar
  32. 32.
    Z. Galil, “String matching in real time,” J. ACM,28, No. 1, 134–146 (1981).Google Scholar
  33. 33.
    E. Reingold, J. Nievergelt, and N. Deo, Combinatorial Algorithms. Theory and Practice, Prentice-Hall, Englewood Cliffs, NJ (1977).Google Scholar
  34. 34.
    J. Gallant, D. Maier, and J. A. Storer, “On finding minimal length superstring,” J. Comput. Syst. Sci.,20, No. 1, 50–58 (1980).Google Scholar
  35. 35.
    M. Aigner, Combinatorial Theory, Springer, Berlin (1979).Google Scholar
  36. 36.
    C. Wrathall, “Complete sets and the polynomial-time hierarchy,” Theor. Comput. Sci.,3, 23–33 (1976).Google Scholar
  37. 37.
    A. Salomaa, Jewels of Formal Language Theory [Russian translation], Mir, Moscow (1986).Google Scholar
  38. 38.
    M. L. Gerver, “Three-valued numbers and digraphs,” Kvant., No. 2, 32–35 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • V. G. Timkovskii

There are no affiliations available

Personalised recommendations