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Dynamic Perfect Hashing: Upper and Lower Bounds


Dietzfelbinger,  Martin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Karlin,  Anna
Max Planck Society;

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Rohnert,  Hans
Max Planck Society;

Tarjan,  Robert E.
Max Planck Society;

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Dietzfelbinger, M., Karlin, A., Mehlhorn, K., Meyer Auf Der Heide, F., Rohnert, H., & Tarjan, R. E. (1991). Dynamic Perfect Hashing: Upper and Lower Bounds.

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