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Fast Algorithms for Finding Disjoint Subsequences with Extremal Densities

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Algorithms and Computation (ISAAC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

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Abstract

We derive fast algorithms for the problem of finding, on the real line, a prescribed number of intervals of maximum total length that contain at most some prescribed number of points from a given point set. Basically this is a typical dynamic programming problem, however, for input sizes much bigger than the two parameters we can improve the obvious time bound by selecting a restricted set of candidate intervals that are sufficient to build some optimal solution. As a byproduct, the same idea improves an algorithm for a similar subsequence problem recently brought up by Chen, Lu and Tang at IWBRA 2005. The problems are motivated by the search for significant patterns in certain biological data. While the algorithmic idea for the asymptotic worst-case bound is rather evident, we also consider further heuristics to save even more time in typical instances. One of them, described in this paper, leads to an apparently open problem of computational geometry flavour (where we are seeking a subquadratic algorithm) which might be interesting in itself.

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Author information

Authors and Affiliations

  1. Department of Molecular Biology, Göteborg University, P.O. Box 462, 40530, Göteborg, Sweden

    Anders Bergkvist

  2. School of Computer Science and Engineering, Chalmers University, 41296, Göteborg, Sweden

    Peter Damaschke

Authors
  1. Anders Bergkvist
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  2. Peter Damaschke
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Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon , Hong Kong

    Xiaotie Deng

  2. Department of Computer Science, University of Texas at Dallas, EE/CS Building, 75083, Richardson, TX, USA

    Ding-Zhu Du

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© 2005 Springer-Verlag Berlin Heidelberg

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Bergkvist, A., Damaschke, P. (2005). Fast Algorithms for Finding Disjoint Subsequences with Extremal Densities. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_72

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  • DOI: https://doi.org/10.1007/11602613_72

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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