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Perfect Hash Families: The Generalization to Higher Indices

In: Discrete Mathematics and Applications

Author

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  • Ryan E. Dougherty

    (United States Military Academy)

  • Charles J. Colbourn

    (Arizona State University)

Abstract

Perfect hash families are often represented as combinatorial arrays encoding partitions of k items into v classes, so that every t or fewer of the items are completely separated by at least a specified number of chosen partitions. This specified number is the index of the hash family. The case when each t-set must be separated at least once has been extensively researched; they arise in diverse applications, both directly and as fundamental ingredients in a column replacement strategy for a variety of combinatorial arrays. In this paper, construction techniques and algorithmic methods for constructing perfect hash families are surveyed, in order to explore extensions to the situation when each t-set must be separated by more than one partition.

Suggested Citation

  • Ryan E. Dougherty & Charles J. Colbourn, 2020. "Perfect Hash Families: The Generalization to Higher Indices," Springer Optimization and Its Applications, in: Andrei M. Raigorodskii & Michael Th. Rassias (ed.), Discrete Mathematics and Applications, pages 177-197, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-55857-4_7
    DOI: 10.1007/978-3-030-55857-4_7
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    Cited by:

    1. Ryan E. Dougherty & Kristoffer Kleine & Michael Wagner & Charles J. Colbourn & Dimitris E. Simos, 2023. "Algorithmic methods for covering arrays of higher index," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.

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