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Closed Hashing is Computable and Optimally Randomizable with Universal Hash Functions
"... Universal hash functions that exhibit c log nwise independence are shown to give a performance in double hashing, uniform hashing and virtually any reasonable generalization of double hashing that has an expected probe count of 1 1\Gammaff +O( 1 n ) for the insertion of the ffnth item into a ta ..."
Abstract

Cited by 6 (1 self)
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Universal hash functions that exhibit c log nwise independence are shown to give a performance in double hashing, uniform hashing and virtually any reasonable generalization of double hashing that has an expected probe count of 1 1\Gammaff +O( 1 n ) for the insertion of the ffnth item into a table of size n, for any fixed ff ! 1. This performance is optimal. These results are derived from a novel formulation that overestimates the expected probe count by underestimating the presence of local items already inserted into the hash table, and from a very sharp analysis of the underlying stochastic structures formed by colliding items. Analogous bounds are attained for the expected rth moment of the probe count, for any fixed r, and linear probing is also shown to achieve a performance with universal hash functions that is equivalent to the fully random case. Categories and Subject Descriptors: E.1 [Data]: Data Structuresarrays; tables; E.2 [Data]: Data Storage Representationsha...
Double Hashing is Computable and Randomizable with Universal Hash Functions
"... Universal hash functions that exhibit c log nwise independence are shown to give a performance in double hashing and virtually any reasonable generalization of double hashing that has an expected probe count of 1/(1alpha) + epsilon for the insertion of the alpha nth item into a table of size n, f ..."
Abstract

Cited by 3 (1 self)
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Universal hash functions that exhibit c log nwise independence are shown to give a performance in double hashing and virtually any reasonable generalization of double hashing that has an expected probe count of 1/(1alpha) + epsilon for the insertion of the alpha nth item into a table of size n, for any fixed alpha 0. This performance is within epsilon of optimal. These results are derived from a novel formulation that overestimates the expected probe count by underestimating the presence of partial items already inserted into the hash table, and from a sharp analysis of the underlying stochastic structures formed by colliding items.