Common Subsequences and Supersequences and their Expected Length

  • Authors:
  • Vlado Dančík

  • Affiliations:
  • Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovakia (e-mail: dancik@turing.upjs.sk)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 1998

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Abstract

Let f(n, k, l) be the expected length of a longest common subsequence of l sequences of length n over an alphabet of size k. It is known that there are constants γ(l)k such that f(n, k, l)→ γ(l)kn as n→∞, and we show that γ(l)k= Θ(k1/l−1) as k→∞. Bounds for the corresponding constants for the expected length of a shortest common supersequence are also presented.