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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


Given two i.i.d. sequences of $n$ letters from a finite alphabet, one can consider the length $L_n$ of the longest sequence which is a subsequence of both the given sequences. It is known that $EL_n$ grows like $\gamma n$ for some $\gamma \in \lbrack 0, 1\rbrack$. Here it is shown that $\gamma n \geq EL_n \geq \gamma n - C(n \log n)^{1/2}$ for an explicit numerical constant $C$ which does not depend on the distribution of the letters. In simulations with $n = 100,000, EL_n/n$ can be determined from $k$ such trials with 95% confidence to within $0.0055/\sqrt k$, and the results here show that $\gamma$ can then be determined with 95% confidence to within $0.0225 + 0.0055/\sqrt k$, for an arbitrary letter distribution.


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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.


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

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

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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