Spatial complexity of oblivious κ-probe hash functions

Jeanette P. Schmidt, Alan Siegel

Research output: Contribution to journalArticlepeer-review


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
Issue number5
StatePublished - 1990

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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