Dynamic Perfect Hashing: Upper and Lower Bounds

  • Authors:
  • Martin Dietzfelbinger;Anna Karlin;Kurt Mehlhorn;Friedhelm Meyer auf der Heide;Hans Rohnert;Robert E. Tarjan

  • Affiliations:
  • -;-;-;-;-;-

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 1994

Quantified Score

Hi-index 0.01

Visualization

Abstract

The dynamic dictionary problem is considered: provide an algorithm for storing a dynamic set, allowing the operations insert, delete, and lookup. A dynamic perfect hashing strategy is given: a randomized algorithm for the dynamic dictionary problem that takes $O(1)$ worst-case time for lookups and $O(1)$ amortized expected time for insertions and deletions; it uses space proportional to the size of the set stored. Furthermore, lower bounds for the time complexity of a class of deterministic algorithms for the dictionary problem are proved. This class encompasses realistic hashing-based schemes that use linear space. Such algorithms have amortized worst-case time complexity $\Omega(\log n)$ for a sequence of $n$ insertions and lookups; if the worst-case lookup time is restricted to $k$, then the lower bound becomes $\Omega(k\cdot n^{1/k})$.