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Calculational Developments of New Parallel Algorithms for Size-Constrained Maximum-Sum Segment Problems

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Functional and Logic Programming (FLOPS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7294))

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Abstract

Parallel algorithms for the one-dimensional and the two-dimensional size-constrained maximum-sum segment problems are proposed. The problem, which is a variant of the classic maximum-sum segment problem, is to locate the segment of the maximum total sum among those whose sizes are in a certain range, say, between l and u. It has several applications including pattern recognition, data mining, and DNA analyses, and the size requirement enables us to exclude trivial or useless results. Our parallel algorithms solve it in time O(n / n/p + log p) for one-dimensional arrays of length n and in time O(n 2(u–l) / p + log p) for n × n two-dimensional arrays on EREW PRAM that consists of p processors. It is worth noting that they achieve asymptotically optimal parallel speedups compared with the best known sequential algorithms that take O(n) and O(n 3) times for the one- and the two-dimensional cases, respectively. Our algorithms are correct by their construction: they are systematically derived from their specifications based on the Bird-Meertens formalism.

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Authors and Affiliations

  1. Research Institute of Electrical Communication, Tohoku University, Japan

    Akimasa Morihata

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  1. Akimasa Morihata
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Editors and Affiliations

  1. Dept. of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9 WE02, 9000, Ghent, Belgium

    Tom Schrijvers

  2. Dept. of Computer Science, University of Freiburg, Georges-Köhler-Allee 106, 79110, Freiburg, Germany

    Peter Thiemann

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Morihata, A. (2012). Calculational Developments of New Parallel Algorithms for Size-Constrained Maximum-Sum Segment Problems. In: Schrijvers, T., Thiemann, P. (eds) Functional and Logic Programming. FLOPS 2012. Lecture Notes in Computer Science, vol 7294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29822-6_18

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  • DOI: https://doi.org/10.1007/978-3-642-29822-6_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29821-9

  • Online ISBN: 978-3-642-29822-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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