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Thermodynamical Approach to the Longest Common Subsequence Problem

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Abstract

We introduce an interacting particle model in a random media and show that this particle process is equivalent to the Longest Common Subsequence (LCS) problem of two binary sequences. We derive a differential equation which links the mean LCS-curve to the average speed of the particles given their density and prove that the average speed of the particles and density converges uniformly on every scale which is somewhat larger than  \(\sqrt{n}\) .

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Authors and Affiliations

  1. University of Bielefeld, Postfach 10 01 31, 33501, Bielefeld, Germany

    Saba Amsalu

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332–0160, USA

    Heinrich Matzinger

  3. Instituto de Matemática, Estatística e Computação Científica, Universidade de Campinas, Caixa Postal 6065, CEP 13083–970, Campinas, SP, Brasil

    Marina Vachkovskaia

Authors
  1. Saba Amsalu
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  2. Heinrich Matzinger
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  3. Marina Vachkovskaia
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Corresponding author

Correspondence to Marina Vachkovskaia.

Additional information

All three authors are grateful to SFB 701. M.V. is grateful to CNPq (304561/2006–1 and 471925/2006–3) and FAPESP (thematic grant 04/07276–2) for partial support.

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Amsalu, S., Matzinger, H. & Vachkovskaia, M. Thermodynamical Approach to the Longest Common Subsequence Problem. J Stat Phys 131, 1103–1120 (2008). https://doi.org/10.1007/s10955-008-9533-z

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  • DOI: https://doi.org/10.1007/s10955-008-9533-z

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