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Longest common subsequences of two random sequences

Published online by Cambridge University Press:  14 July 2016

Vacláv Chvátal  and
David Sankoff
Vacláv Chvátal
Affiliation:
Université de Montréal
David Sankoff
Affiliation:
Université de Montréal
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Summary

Given two random k-ary sequences of length n, what is f(n,k), the expected length of their longest common subsequence? This problem arises in the study of molecular evolution. We calculate f(n,k) for all k, where n ≦ 5, and f(n,2) where n ≦ 10. We study the limiting behaviour of n–1f(n,k) and derive upper and lower bounds on these limits for all k. Finally we estimate by Monte-Carlo methods f(100,k), f(1000,2) and f(5000,2).

Keywords

RANDOM SEQUENCESCOMMON SUBSEQUENCESMATCHES
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 306 - 315
Copyright
Copyright © Applied Probability Trust 1975 

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References

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