TY - CHAP
T1 - Perfect Hash Families
T2 - The Generalization to Higher Indices
AU - Dougherty, Ryan E.
AU - Colbourn, Charles J.
N1 - Funding Information:
Acknowledgments This work is supported in part by the U.S. National Science Foundation grants #1421058 and #1813729. Thanks to Randy Compton, Stephanie Forrest, Daniel Horsley, Erin Lanus, Kaushik Sarkar, and Violet Syrotiuk for helpful discussions, and to an anonymous reviewer for very useful comments.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-030-55857-4_7
DO - 10.1007/978-3-030-55857-4_7
M3 - Chapter
AN - SCOPUS:85096548421
T3 - Springer Optimization and Its Applications
SP - 177
EP - 197
BT - Springer Optimization and Its Applications
PB - Springer
ER -