# Improved bounds on the average length of longest common subsequences

@inproceedings{Lueker2009ImprovedBO,
title={Improved bounds on the average length of longest common subsequences},
author={George S. Lueker},
booktitle={JACM},
year={2009}
}
• G. S. Lueker
• Published in JACM 12 January 2003
• Computer Science
It has long been known [Chvátal and Sankoff 1975] that the average length of the longest common subsequence of two random strings of length <i>n</i> over an alphabet of size <i>k</i> is asymptotic to γ<sub><i>k</i></sub><i>n</i> for some constant γ<sub><i>k</i></sub> depending on <i>k</i>. The value of these constants remains unknown, and a number of papers have proved upper and lower bounds on them. We discuss techniques, involving numerical calculations with recurrences on many variables, for…

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