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.