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On Suboptimal LCS-alignments for Independent Bernoulli Sequences with Asymmetric Distributions

Author

Listed:
  • Stanislaw Barder

    (University of Bielefeld)

  • Jüri Lember

    (University of Tartu)

  • Heinrich Matzinger

    (Georgia Tech)

  • Märt Toots

    (University of Tartu)

Abstract

Let X = X 1 ... X n and Y = Y 1 ... Y n be two binary sequences with length n. A common subsequence of X and Y is any subsequence of X that at the same time is a subsequence of Y; The common subsequence with maximal length is called the longest common subsequence (LCS) of X and Y. LCS is a common tool for measuring the closeness of X and Y. In this note, we consider the case when X and Y are both i.i.d. Bernoulli sequences with the parameters ϵ and 1 − ϵ, respectively. Hence, typically the sequences consist of large and short blocks of different colors. This gives an idea to the so-called block-by-block alignment, where the short blocks in one sequence are matched to the long blocks of the same color in another sequence. Such and alignment is not necessarily a LCS, but it is computationally easy to obtain and, therefore, of practical interest. We investigate the asymptotical properties of several block-by-block type of alignments. The paper ends with the simulation study, where the of block-by-block type of alignments are compared with the LCS.

Suggested Citation

  • Stanislaw Barder & Jüri Lember & Heinrich Matzinger & Märt Toots, 2012. "On Suboptimal LCS-alignments for Independent Bernoulli Sequences with Asymmetric Distributions," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 357-382, June.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:2:d:10.1007_s11009-010-9206-7
    DOI: 10.1007/s11009-010-9206-7
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    References listed on IDEAS

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    1. Hilary S. Booth & Shevarl F. MacNamara & Ole M. Nielsen & Susan R. Wilson, 2004. "An Iterative Approach to Determining the Length of the Longest Common Subsequence of Two Strings," Methodology and Computing in Applied Probability, Springer, vol. 6(4), pages 401-421, December.
    2. Durringer, Clement & Hauser, Raphael & Matzinger, Heinrich, 2008. "Approximation to the mean curve in the LCS problem," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 629-648, April.
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    Cited by:

    1. Lember, Jüri & Matzinger, Heinrich & Sova, Joonas & Zucca, Fabio, 2018. "Lower bounds for moments of global scores of pairwise Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1678-1710.

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    1. Lember, Jüri & Matzinger, Heinrich & Sova, Joonas & Zucca, Fabio, 2018. "Lower bounds for moments of global scores of pairwise Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1678-1710.

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