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Sequence Covering Arrays and Linear Extensions

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Combinatorial Algorithms (IWOCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8986))

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  • International Workshop on Combinatorial Algorithms

Abstract

Covering subsequences by sets of permutations arises in numerous applications. Given a set of permutations that cover a specific set of subsequences, it is of interest not just to know how few permutations can be used, but also to find a set of size equal to or close to the minimum. These permutation construction problems have proved to be computationally challenging; few explicit constructions have been found for small sets of permutations of intermediate length, mostly arising from greedy algorithms. A different strategy is developed here. Starting with a set that covers the specific subsequences required, we determine local changes that can be made in the permutations without losing the required coverage. By selecting these local changes (using linear extensions) so as to make one or more permutations less ‘important’ for coverage, the method attempts to make a permutation redundant so that it can be removed and the set size reduced. A post-optimization method to do this is developed, and preliminary results on sequence covering arrays show that it is surprisingly effective.

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Acknowledgments

Thanks to Sunil Chandran, Marty Golumbic, Rogers Mathew, and Deepak Rajendraprasad for interesting discussions about permutation coverings and geometric representations of graphs and hypergraphs.

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Authors and Affiliations

  1. School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, P.O. Box 878809, Tempe, AZ, 85287, USA

    Patrick C. Murray & Charles J. Colbourn

Authors
  1. Patrick C. Murray
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  2. Charles J. Colbourn
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Corresponding author

Correspondence to Charles J. Colbourn .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

    Kratochvíl Jan

  2. University of Newcastle, Newcastle, New South Wales, Australia

    Mirka Miller

  3. University of Minnesota, Duluth Department of Mathematics, Duluth, Minnesota, USA

    Dalibor Froncek

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Murray, P.C., Colbourn, C.J. (2015). Sequence Covering Arrays and Linear Extensions. In: Jan, K., Miller, M., Froncek, D. (eds) Combinatorial Algorithms. IWOCA 2014. Lecture Notes in Computer Science(), vol 8986. Springer, Cham. https://doi.org/10.1007/978-3-319-19315-1_24

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  • DOI: https://doi.org/10.1007/978-3-319-19315-1_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19314-4

  • Online ISBN: 978-3-319-19315-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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