Standard deviation of the longest common subsequence
Probability
2009-07-30 v1
Abstract
Let be the length of the longest common subsequence of two independent i.i.d. sequences of Bernoulli variables of length . We prove that the order of the standard deviation of is , provided the parameter of the Bernoulli variables is small enough. This validates Waterman's conjecture in this situation [Philos. Trans. R. Soc. Lond. Ser. B 344 (1994) 383--390]. The order conjectured by Chvatal and Sankoff [J. Appl. Probab. 12 (1975) 306--315], however, is different.
Keywords
Cite
@article{arxiv.0907.5137,
title = {Standard deviation of the longest common subsequence},
author = {Jüri Lember and Heinrich Matzinger},
journal= {arXiv preprint arXiv:0907.5137},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AOP436 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)