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Common Subsequences and Supersequences and their Expected Length

Published online by Cambridge University Press:  01 December 1998

VLADO DANČÍK
Affiliation:
Current address: Millennium Pharmaceuticals, 40 Erie Street, Cambridge, MA 02139–4254, USA (e-mail: dancik@mpi.com)

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.

Type
Research Article
Copyright
1998 Cambridge University Press

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