20 research outputs found
Deterministic and efficient minimal perfect hashing schemes
Neste trabalho apresentamos versões determinísticas para os esquemasde hashing de Botelho, Kohayakawa e Ziviani (2005) e por Botelho, Pagh e Ziviani(2007). Também respondemos a um problema deixado em aberto no primeiro dostrabalhos, relacionado à prova da corretude e à análise de complexidade do esquemapor eles proposto. As versões determinísticas desenvolvidas foram implementadase testadas sobre conjuntos de dados com até 25.000.000 de chaves, e os resultadosverificados se mostraram equivalentes aos dos algoritmos aleatorizados originais
Algebraic Methods in the Congested Clique
In this work, we use algebraic methods for studying distance computation and
subgraph detection tasks in the congested clique model. Specifically, we adapt
parallel matrix multiplication implementations to the congested clique,
obtaining an round matrix multiplication algorithm, where
is the exponent of matrix multiplication. In conjunction
with known techniques from centralised algorithmics, this gives significant
improvements over previous best upper bounds in the congested clique model. The
highlight results include:
-- triangle and 4-cycle counting in rounds, improving upon the
triangle detection algorithm of Dolev et al. [DISC 2012],
-- a -approximation of all-pairs shortest paths in
rounds, improving upon the -round -approximation algorithm of Nanongkai [STOC 2014], and
-- computing the girth in rounds, which is the first
non-trivial solution in this model.
In addition, we present a novel constant-round combinatorial algorithm for
detecting 4-cycles.Comment: This is work is a merger of arxiv:1412.2109 and arxiv:1412.266
Separating hash families with large universe
Separating hash families are useful combinatorial structures which generalize
several well-studied objects in cryptography and coding theory. Let
denote the maximum size of universe for a -perfect hash family of length
over an alphabet of size . In this paper, we show that for all , which answers an open problem about separating
hash families raised by Blackburn et al. in 2008 for certain parameters.
Previously, this result was known only for . Our proof is obtained by
establishing the existence of a large set of integers avoiding nontrivial
solutions to a set of correlated linear equations.Comment: 17 pages, no figur