## Closed Hashing is Computable and Optimally Randomizable with Universal Hash Functions (0)

Citations: | 6 - 1 self |

### BibTeX

@MISC{Siegel_closedhashing,

author = {Alan Siegel and Jeanette P. Schmidt},

title = {Closed Hashing is Computable and Optimally Randomizable with Universal Hash Functions},

year = {}

}

### OpenURL

### Abstract

Universal hash functions that exhibit c log n-wise 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 ffn-th 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 r-th 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 Structures---arrays; tables; E.2 [Data]: Data Storage Representations---ha...