Perfect Hash Families: The Generalization to Higher Indices

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 speci fied number of the 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.