Heaviest increasing/common subsequence problems

  • Guy Jacobson
  • Kiem-Phong Vo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 644)


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.


Weight Function Edit Distance Young Tableau Plane Partition Position List 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Guy Jacobson
    • 1
  • Kiem-Phong Vo
    • 1
  1. 1.AT&T Bell LaboratoriesMurray Hill

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