Open Access
November, 1994 The Rate of Convergence of the Mean Length of the Longest Common Subsequence
Kenneth S. Alexander
Ann. Appl. Probab. 4(4): 1074-1082 (November, 1994). DOI: 10.1214/aoap/1177004903

Abstract

Given two i.i.d. sequences of n letters from a finite alphabet, one can consider the length Ln of the longest sequence which is a subsequence of both the given sequences. It is known that ELn grows like γn for some γ[0,1]. Here it is shown that γnELnγnC(nlogn)1/2 for an explicit numerical constant C which does not depend on the distribution of the letters. In simulations with n=100,000,ELn/n can be determined from k such trials with 95% confidence to within 0.0055/k, and the results here show that γ can then be determined with 95% confidence to within 0.0225+0.0055/k, for an arbitrary letter distribution.

Citation

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Kenneth S. Alexander. "The Rate of Convergence of the Mean Length of the Longest Common Subsequence." Ann. Appl. Probab. 4 (4) 1074 - 1082, November, 1994. https://doi.org/10.1214/aoap/1177004903

Information

Published: November, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0812.60014
MathSciNet: MR1304773
Digital Object Identifier: 10.1214/aoap/1177004903

Subjects:
Primary: 60C05

Keywords: First-passage percolation , Longest common subsequence , subadditivity‎

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.4 • No. 4 • November, 1994
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