Graphs, hypergraphs and hashing

Havas, George; Majewski, Bohdan S.; Wormald, Nicholas C.; Czech, Zbigniew J.

doi:10.1007/3-540-57899-4_49

Cited by 15 publications

(9 citation statements)

References 40 publications

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“…A recently discovered algorithm for generating minimal perfect hash functions uses random r-uniform hypergraphs, in which the threshold of the appearance of the r-analogue of a cycle is crucial (see Havas et al [13], where rough estimates on the threshold are derived). The problem of determining this threshold is very similar to that for the k-core of a random graph.…”

Section: Introductionmentioning

confidence: 99%

Sudden Emergence of a Giantk-Core in a Random Graph

Pittel

Spencer

Wormald

1996

Journal of Combinatorial Theory, Series B

421

485

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Section: Introductionmentioning

confidence: 99%

Sudden Emergence of a Giantk-Core in a Random Graph

Pittel

Spencer

Wormald

1996

Journal of Combinatorial Theory, Series B

421

485

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“…A further improvement consists in using hypergraphs (generalization of graphs in higher dimensions): As soon as |V| > 1.23 × |E|, a random 3-hypergraph has an "acyclic" property with a probability of almost 1 [30], [32]. In practice, assignment and computation of phf on 3-hypergraphs are…”

Section: B Graph-based Perfect Hash Functionsmentioning

confidence: 99%

“…• Checking the acyclicity can be done with the algorithm of [32]. In the unlikely cases where the graph is not acyclic, another random graph can be generated by choosing three other hash functions.…”

Section: A Indexation With 3-hypergraphs Generationmentioning

confidence: 99%

Perfect Hashing Structures for Parallel Similarity Searches

Tran

Giraud

Varré

2015

2015 IEEE International Parallel and Distributed Processing Symposium Workshop

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Abstract-Seed-based heuristics have proved to be efficient for studying similarity between genetic databases with billions of base pairs. This paper focuses on algorithms and data structures for the filtering phase in seed-based heuristics, with an emphasis on efficient parallel GPU/manycores implementation. We propose a 2-stage index structure which is based on neighborhood indexing and perfect hashing techniques. This structure performs a filtering phase over the neighborhood regions around the seeds in constant time and avoid as much as possible random memory accesses and branch divergences. Moreover, it fits particularly well on parallel SIMD processors, because it requires intensive but homogeneous computational operations. Using this data structure, we developed a fast and sensitive OpenCL prototype read mapper.

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“…It is known that finding a perfect hash function for sets with n keys cannot be done in o(n) time [3], although many O(n)-time perfect hashing schemes are known from literature [2,10,11,12]. For example, the randomized hashing scheme presented in [3], which maps the n keys to the edges of an acyclic graph on 2.09n vertices and then uses a depth-first search to label the edges with the values 1, .…”

Section: Related Workmentioning

confidence: 99%

Deterministic and efficient minimal perfect hashing schemes

Zatesko

Donadelli

2013

RITA

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This paper presents deterministic versions to the hashing schemes of Botelho, Kohayakawa and Ziviani (2005) and Botelho, Pagh and Ziviani (2007), also proves a statement left as open problem in the former work, related to the correctness proof and to the complexity analysis of their scheme. Our deterministic variants have been implemented and executed over datasets with up to 25,000,000 keys and have brought equivalent performance results between the deterministic and the original randomized algorithms. Resumo: Neste trabalho apresentamos versões determinísticas para os esquemas de hashing de Botelho, Kohayakawa e Ziviani (2005) e de Botelho, Pagh e Ziviani (2007). Também respondemos a um problema deixado em aberto no primeiro dos trabalhos, relacionado à prova da corretude e à análise de complexidade do esquema por eles proposto. As versões determinísticas desenvolvidas foram implementadas e testadas sobre conjuntos de dados com até 25.000.000 de chaves, e os resultados verificados se mostraram equivalentes aos dos algoritmos aleatorizados originais.

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Graphs, hypergraphs and hashing

Cited by 15 publications

References 40 publications

Sudden Emergence of a Giantk-Core in a Random Graph

Sudden Emergence of a Giantk-Core in a Random Graph

Perfect Hashing Structures for Parallel Similarity Searches

Deterministic and efficient minimal perfect hashing schemes

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