Skip to main content
SpringerLink
Log in
Book cover

Annual Symposium on Combinatorial Pattern Matching

CPM 1992: Combinatorial Pattern Matching pp 52–66Cite as

Heaviest increasing/common subsequence problems

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 644))

Abstract

In this paper, we define the heaviest increasing subsequence (HIS) and heaviest common subsequence (HCS) problems as natural generalizations of the well-studied longest increasing subsequence (LIS) and longest common subsequence (LCS) problems. We show how the famous Robinson-Schensted correspondence between permutations and pairs of Young tableaux can be extended to compute heaviest increasing subsequences. Then, we point out a simple weight-preserving correspondence between the HIS and HCS problems. ¿ From this duality between the two problems, the Hunt-Szymanski LCS algorithm can be seen as a special case of the Robinson-Schensted algorithm. Our HIS algorithm immediately gives rise to a Hunt-Szymanski type of algorithm for HCS with the same time complexity. When weights are position-independent, we can exploit the structure inherent in the HIS-HCS correspondence to further refine the algorithm. This gives rise to a specialized HCS algorithm of the same type as the Apostolico-Guerra LCS algorithm.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. V. Aho, D. S. Hirschberg, and J. D. Ullman. Bounds on the complexity of the longest common subsequence problem. JACM, 23(1):1–12, 1976.

    Google Scholar 

  2. A. Apostolico and C Guerra. The longest common subsequence problem revisited. Algorithmica, 2:315–336, 1987.

    Google Scholar 

  3. Francis Y. L. Chin and C. K. Poon. A fast algorithm for computing longest common subsequences of small alphabet size. Journal of Information Processing, 13(4):463–469, 1990.

    Google Scholar 

  4. Michael L. Fredman. On computing the length of longest increasing subsequences. Discrete Mathematics, 11:29–35, 1975.

    Google Scholar 

  5. E. Gansner. Matrix Correspondences and the Enumeration of Plane Partitions. PhD thesis, MIT, Cambridge, MA, 1978.

    Google Scholar 

  6. M. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, 1980.

    Google Scholar 

  7. Daniel S. Hirschberg. A linear space algorithm for computing maximal common subsequences. CACM, 18(6):341–343, 1975.

    Google Scholar 

  8. Daniel S. Hirschberg. Algorithms for the longest common subsequence problem. JACM, 24(4):664–675, 1977.

    Google Scholar 

  9. W. J. Hsu and M. W. Du. New algorithms for the LCS problem. JCSS, 29:133–152, 1984.

    Google Scholar 

  10. J. W. Hunt and M. D. McIlroy. An algorithm for differential file comparison. Computer Science Technical Report 41, Bell Laboratories, 1975.

    Google Scholar 

  11. James W. Hunt and Thomas G. Szymanski. A fast algorithm for computing longest common subsequences. CACM, 20(5):350–353, 1977.

    Google Scholar 

  12. D. Knuth. The Art of Computer Programming, volume 3. Addison-Wesley, Reading, MA, 1973.

    Google Scholar 

  13. William J. Masek and Michael S. Patterson. A faster algorithm computing string edit distances. JCSS, 20:18–31, 1980.

    Google Scholar 

  14. Eugene W. Myers. An O(ND) difference algorithm and its variations. Algorithmica, 1:251–266, 1986.

    Google Scholar 

  15. N. Nakatsu, Y. Kambayashi, and S. Yajima. A longest common subsequence algorithm suitable for similar text strings. Acta Informatica, 18:171–179, 1982.

    Google Scholar 

  16. G. De B. Robinson. On the representations of the symmetric group. American J. Math., 60:745–760, 1938.

    Google Scholar 

  17. D. Sankoff and J.B. Kruskal. Time Warps, String Edits and Macromolecules: The Theory and Practice of Sequence Comparisons. Addison Wesley, Reading, MA, 1983.

    Google Scholar 

  18. C. Schensted. Largest increasing and decreasing subsequences. Canadian J. Math., 13:179–191, 1961.

    Google Scholar 

  19. D. Sleator and R. Tarjan. Self-adjusting binary trees. JACM, 32:652–686, 1985.

    Google Scholar 

  20. R. Stanley. Theory and applications of plane partitions. Stud. Applied Math., 50:259–279, 1971.

    Google Scholar 

  21. K.-P. Vo. More <curses>: the <screen> library. Technical report, AT&T Bell Laboratories, 1986.

    Google Scholar 

  22. K.-P. Vo and R. Whitney. Tableaux and matrix correspondences. J. of Comb. Theory, Series A, 35:323–359, 1983.

    Google Scholar 

  23. R. A. Wagner and M. J. Fischer. The string-to-string correction problem. JACM, 21(1):168–173, 1974.

    Google Scholar 

  24. Sun Wu, Udi Manber, Gene Myers, and Webb Miller. An O(NP) sequence comparison algorithm. Information Processing Letters, 35(6):317–323, 1990.

    Google Scholar 

  25. A. Young. The collected papers of alfred young. Math. Exp., 21, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AT&T Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ

    Guy Jacobson & Kiem-Phong Vo

Authors
  1. Guy Jacobson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kiem-Phong Vo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alberto Apostolico Maxime Crochemore Zvi Galil Udi Manber

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jacobson, G., Vo, KP. (1992). Heaviest increasing/common subsequence problems. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds) Combinatorial Pattern Matching. CPM 1992. Lecture Notes in Computer Science, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56024-6_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-56024-6_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56024-1

  • Online ISBN: 978-3-540-47357-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation