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Efficient Conditional Expectation Algorithms for Constructing Hash Families

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Combinatorial Algorithms (IWOCA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7056))

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Abstract

Greedy methods for solving set cover problems provide a guarantee on how close the solution is to optimal. Consequently they have been widely explored to solve set cover problems arising in the construction of various combinatorial arrays, such as covering arrays and hash families. In these applications, however, a naive set cover formulation lists a number of candidate sets that is exponential in the size of the array to be produced. Worse yet, even if candidate sets are not listed, finding the ‘best’ candidate set is NP-hard. In this paper, it is observed that one does not need a best candidate set to obtain the guarantee — an average candidate set will do. Finding an average candidate set can be accomplished using a technique employing the method of conditional expectations for a wide range of set cover problems arising in the construction of hash families. This yields a technique for constructing hash families, with a wide variety of properties, in time polynomial in the size of the array produced.

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Author information

Authors and Affiliations

  1. Computing, Informatics, and Decision Systems Engineering, Arizona State University, PO Box 878809, Tempe, AZ, 85287-8809, U.S.A.

    Charles J. Colbourn

Authors
  1. Charles J. Colbourn
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Editor information

Editors and Affiliations

  1. Digital Ecosystems & Business Intelligence Institute, Curtin University, Perth, Australia

    Costas S. Iliopoulos

  2. Department of Computing and Software Information Technology Building, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    William F. Smyth

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© 2011 Springer-Verlag Berlin Heidelberg

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Colbourn, C.J. (2011). Efficient Conditional Expectation Algorithms for Constructing Hash Families. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_12

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  • DOI: https://doi.org/10.1007/978-3-642-25011-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25010-1

  • Online ISBN: 978-3-642-25011-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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