Minimal perfect hash functions provide space-efficient and collision-free hashing on static sets. Existing algorithms and implementations that build such functions have practical limitations on the number of input elements they can process, due to high construction time, RAM or external memory usage. We revisit a simple algorithm and show that it is highly competitive with the state of the art,...

In Image Database Systems, symbolic pictures are represented by 2D strings that are converted into triples. Each triple is mapped to a unique hash address for timely retrieval of pictures, reducing the pattern-matching problem corresponding to a query to that of computation of hash function. The values associated with the picture objects are used to compute hash addresses for triples developed ...

In this paper, we consider explicit constructions of perfect hash families using combi-natorial methods. We provide several direct constructions from combinatorial structures related to orthogonal arrays. We also simplify and generalize a recursive construction due to Atici, Magliversas, Stinson and Wei 3]. Using similar methods, we also obtain eecient constructions for separating hash families...

In this paper we propose a simple and efficient data structure yielding a perfect hashing of quite general arrays. The data structure is named phorma, which is an acronym for perfectly hashable order restricted multidimensional array.

A graph G is called Berge if neither G nor its complement contains a chordless cycle with an odd number of nodes. The famous Berge’s Strong Perfect Graph Conjecture asserts that every Berge graph is perfect. A chair is a graph with nodes {a, b, c, d, e} and edges {ab, bc, cd, eb}. We prove that a Berge graph with no induced chair (chair-free) is perfect or, equivalently, that the Strong Perfect...

A new algorithm for generating order preserving minimal perfect hash functions is presented. The algorithm is probabilistic, involving generation of random graphs. It uses expected linear time and requires a linear number words to represent the hash function, and thus is optimal up to constant factors. It runs very fast in practice.

We propose a new scheme for sharing symmetric key operations among a set of participants according to a ) , ( n t threshold access structure. We focus on anonymity properties of this scheme and show that this scheme provides improved values of anonymity measures than the existing ones. In particular, the scheme can provide optimal and equitable participant anonymity when it is based on balanced...

The Lovász Local Lemma is a useful tool in the “probabilistic method” that has found many applications in combinatorics. In this paper, we discuss applications of the Lovász Local Lemma to some combinatorial set systems and arrays, including perfect hash families, separating hash families, -free systems, splitting systems, and generalized cover-free families. We obtain improved bounds for some ...

Minimal perfect hash functions are used for memory efficient storage and fast retrieval of items from static sets. We present an infinite family of efficient and practical algorithms for generating minimal perfect hash functions which allow an arbitrary order to be specified for the keys. We show that almost all members of the family are space and time optimal, and we identify the one with mini...