### Abstract

The problem of constructing a dense static hash-based lookup table T for a set of n elements belonging to a universe U ={0,1,2,...,m - 1} is considered. Nearly tight bounds on the spatial complexity of oblivious O(1)-probe hash functions, which are defined to depend solely on their search key argument, are provided. This establishes a significant gap between oblivious and nonoblivious search. In particular, the results include the following: A lower bound showing that oblivious κ-probe hash functions require a program size of Ω((n/k^{2})e^{-k}+ log log m) bits, on average. A probabilistic construction of a family of oblivious κ-probe hash functions that can be specified in O(ne^{-k}+ log log m) bits, which nearly matches the above lower bound. A variation of an explicit O(1) time 1-probe (perfect) hash function family that can be specified in O(n+log log m) bits, which is tight to within a constant factor of the lower bound.

Original language | English (US) |
---|---|

Pages (from-to) | 775-786 |

Number of pages | 12 |

Journal | SIAM Journal on Computing |

Volume | 19 |

Issue number | 5 |

State | Published - Oct 1990 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Theoretical Computer Science

### Cite this

*SIAM Journal on Computing*,

*19*(5), 775-786.

**Spatial complexity of oblivious κ-probe hash functions.** / Schmidt, Jeanette P.; Siegel, Alan.

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 19, no. 5, pp. 775-786.

}

TY - JOUR

T1 - Spatial complexity of oblivious κ-probe hash functions

AU - Schmidt, Jeanette P.

AU - Siegel, Alan

PY - 1990/10

Y1 - 1990/10

N2 - The problem of constructing a dense static hash-based lookup table T for a set of n elements belonging to a universe U ={0,1,2,...,m - 1} is considered. Nearly tight bounds on the spatial complexity of oblivious O(1)-probe hash functions, which are defined to depend solely on their search key argument, are provided. This establishes a significant gap between oblivious and nonoblivious search. In particular, the results include the following: A lower bound showing that oblivious κ-probe hash functions require a program size of Ω((n/k2)e-k+ log log m) bits, on average. A probabilistic construction of a family of oblivious κ-probe hash functions that can be specified in O(ne-k+ log log m) bits, which nearly matches the above lower bound. A variation of an explicit O(1) time 1-probe (perfect) hash function family that can be specified in O(n+log log m) bits, which is tight to within a constant factor of the lower bound.

AB - The problem of constructing a dense static hash-based lookup table T for a set of n elements belonging to a universe U ={0,1,2,...,m - 1} is considered. Nearly tight bounds on the spatial complexity of oblivious O(1)-probe hash functions, which are defined to depend solely on their search key argument, are provided. This establishes a significant gap between oblivious and nonoblivious search. In particular, the results include the following: A lower bound showing that oblivious κ-probe hash functions require a program size of Ω((n/k2)e-k+ log log m) bits, on average. A probabilistic construction of a family of oblivious κ-probe hash functions that can be specified in O(ne-k+ log log m) bits, which nearly matches the above lower bound. A variation of an explicit O(1) time 1-probe (perfect) hash function family that can be specified in O(n+log log m) bits, which is tight to within a constant factor of the lower bound.

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M3 - Article

AN - SCOPUS:0025507834

VL - 19

SP - 775

EP - 786

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 5

ER -