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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 order preserving minimal perfect hash functions. We show that almost all members of the family construct space and time optimal order preserving minimal perfect… (More)

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 study the complexity of expressing the greatest common divisor of n positive numbers as a linear combination of the numbers. We prove the NP-completeness of finding an optimal set of multipliers with respect to either the L0 metric or the L∞ norm. We present and analyze a new method for expressing the gcd of n numbers as their linear combination and give… (More)

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x s m are given integers. The method… (More)

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… (More)

We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations—explosive growth in size of intermediate entries. We present a new algorithm with excellent performance. We investigate the complexity of such… (More)

We consider algorithms for computing the Hermite normal form of integer matrices. Various different strategies have been proposed, primarily trying to avoid the major obstacle that occurs in such computations — explosive growth in size of intermediate entries. We analyze some methods for computing the Hermite normal form and we show the intractability of… (More)

An improved method for expressing the greatest common divisor of n numbers as an integer linear combination of the numbers is presented and analyzed, both theoretically and practically. The performance of this algorithm is compared with other methods, indicating substantial improvements in the size of the solution. The results are given in the light of the… (More)