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Annual Symposium on Combinatorial Pattern Matching

CPM 2012: Combinatorial Pattern Matching pp 149–158Cite as

Near Linear Time Construction of an Approximate Index for All Maximum Consecutive Sub-sums of a Sequence

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7354))

Abstract

We present a novel approach for computing all maximum consecutive subsums in a sequence of positive integers in near linear time. Solutions for this problem over binary sequences can be used for reporting existence (and possibly one occurrence) of Parikh vectors in a bit string. Recently, several attempts have been tried to build indexes for all Parikh vectors of a binary string in subquadratic time. However, to the best of our knowledge, no algorithm is know to date which can beat by more than a polylogarithmic factor the natural Θ(n 2) exhaustive procedure. Our result implies an approximate construction of an index for all Parikh vectors of a binary string in O(n 1 + η) time, for any constant η > 0. Such index is approximate, in the sense that it leaves a small chance for false positives, i.e., Parikh vectors might be reported which are not actually present in the string. No false negative is possible. However, we can tune the parameters of the algorithm so that we can strictly control such a chance of error while still guaranteeing strong sub-quadratic running time.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Salerno, Italy

    Ferdinando Cicalese

  2. Department of Informatics, PUC-Rio, Rio de Janeiro, Brazil

    Eduardo Laber

  3. Department of Computer Science, University of Haifa, Israel

    Oren Weimann

  4. Department of Mathematics, University of Haifa, Israel

    Raphael Yuster

Authors
  1. Ferdinando Cicalese
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  2. Eduardo Laber
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  3. Oren Weimann
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  4. Raphael Yuster
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Helsinki, Gustaf Hällström Katu 2b, P.O. Box 68, 00014, Helsinki, Finland

    Juha Kärkkäinen

  2. Faculty of Technology, University of Bielefeld, Universitätsstraße 25, 33615, Bielefeld, Germany

    Jens Stoye

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Cicalese, F., Laber, E., Weimann, O., Yuster, R. (2012). Near Linear Time Construction of an Approximate Index for All Maximum Consecutive Sub-sums of a Sequence. In: Kärkkäinen, J., Stoye, J. (eds) Combinatorial Pattern Matching. CPM 2012. Lecture Notes in Computer Science, vol 7354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31265-6_12

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  • DOI: https://doi.org/10.1007/978-3-642-31265-6_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31264-9

  • Online ISBN: 978-3-642-31265-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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