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Contributing USMA Research Unit(s)
Electrical Engineering and Computer Science
Perfect hash families are often represented as combinatorial arrays encoding partitions of kitems 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.
Dougherty, Ryan and Colbourn, Charles J., "Perfect Hash Families: The Generalization to Higher Indices" (2020). West Point Books. 25.