Dynamic Perfect Hashing: Upper and Lower Bounds

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 $OMEGA (k^cdot^n sup 1/k$).

This technical report has been published as

Dynamic Perfect Hashing: Upper and Lower Bounds. Martin
Dietzfelbinger, Anna R. Karlin, Kurt Mehlhorn,
Friedhelm Meyer auf der Heide, Hans Rohnert and
Robert E. Tarjan,

Proc. 29th Annual IEEE Symp. on Foundations of Computer
Science (1988), 524-531 and

SIAM J. Comput. 23 (1994) 738-761.