Expected length of the longest common subsequence for large alphabets
Combinatorics
2007-05-23 v1 Probability
Abstract
We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.
Keywords
Cite
@article{arxiv.math/0308234,
title = {Expected length of the longest common subsequence for large alphabets},
author = {Marcos Kiwi and Martin Loebl and Jiri Matousek},
journal= {arXiv preprint arXiv:math/0308234},
year = {2007}
}
Comments
14 pages, 1 figure, LaTex