
Program Systems: Theory and Applications, 2016, Volume 7, Issue 1, Pages 201–208
(Mi ps207)




This article is cited in 2 scientific papers (total in 2 papers)
Mathematical Foundations of Programming
A picture of common subsequence length for two random strings over an alphabet of 4 symbols
S. V. Znamenskij^{} ^{} Ailamazyan Program System Institute of RAS
Abstract:
The maximal length of longest common subsequence (LCS) for a couple of random finite sequences over an alphabet of 4 characters was considered as a random function of the sequences lengths $m$ and $n$.
Exact probability distributions tables are presented for all couples of length in a range $2<m+n<19$.
The graphs of expected value and standard deviation as a functions of length are shown in linear perspective which presents the behaviour of large lengths at the horizon.
In order to illustrate behaviour on large lengths, the results of numeric simulation for $m+n=32$, 512, 8192 and 131072 are also shown on the same graphs.
The presented graph of expected value dependency of $m$ and $n$ looks to have asymptotic right circular cone.
The variance looks alike growing as $(n+m)^{\frac34}$.
Key words and phrases:
similarity of strings, sequence alignment, edit distance, LCS, Levenshtein metric.
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UDC:
004.416 Received: 25.12.2015 Accepted: 28.03.2016
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Citation:
S. V. Znamenskij, “A picture of common subsequence length for two random strings over an alphabet of 4 symbols”, Program Systems: Theory and Applications, 7:1 (2016), 201–208
Citation in format AMSBIB
\Bibitem{Zna16}
\by S.~V.~Znamenskij
\paper A picture of common subsequence length for two random strings over an alphabet of 4 symbols
\jour Program Systems: Theory and Applications
\yr 2016
\vol 7
\issue 1
\pages 201208
\mathnet{http://mi.mathnet.ru/ps207}
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This publication is cited in the following articles:

S. V. Znamenskii, “Priblizhenie dliny naibolshei obschei podposledovatelnosti pary sluchainykh strok”, Programmnye sistemy: teoriya i prilozheniya, 7:4 (2016), 347–358

Sergej V. Znamenskij, “A formula for the mean length of the longest common subsequence”, Zhurn. SFU. Ser. Matem. i fiz., 10:1 (2017), 71–74

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