Spatial complexity of oblivious κ-probe hash functions

Jeanette P. Schmidt, Alan Siegel

Research output: Contribution to journalArticle

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/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.

Original languageEnglish (US)
Pages (from-to)775-786
Number of pages12
JournalSIAM Journal on Computing
Volume19
Issue number5
StatePublished - Oct 1990

Fingerprint

Hash functions
Hash Function
Probe
Lower bound
Table lookup
Look-up Table
Family

ASJC Scopus subject areas

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

Cite this

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

In: SIAM Journal on Computing, Vol. 19, No. 5, 10.1990, p. 775-786.

Research output: Contribution to journalArticle

Schmidt, Jeanette P. ; Siegel, Alan. / Spatial complexity of oblivious κ-probe hash functions. In: SIAM Journal on Computing. 1990 ; Vol. 19, No. 5. pp. 775-786.
@article{e8cc5cf53b2f4ecc8a749076508554e1,
title = "Spatial complexity of oblivious κ-probe hash functions",
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/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.",
author = "Schmidt, {Jeanette P.} and Alan Siegel",
year = "1990",
month = "10",
language = "English (US)",
volume = "19",
pages = "775--786",
journal = "SIAM Journal on Computing",
issn = "0097-5397",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",

}

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.

UR - http://www.scopus.com/inward/record.url?scp=0025507834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025507834&partnerID=8YFLogxK

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 -