Dynamic perfect hashing

Dynamic perfect hashing is a programming technique for resolving collisions in a hash table data structure .

In this method, the entries that hash to the same slot of the table are organized as separate second-level hash table. If there are k entries in this set, the second-level table is allocated with k² slots, and its hash function is selected at random from a universal hash function set so that it is collision-free (i.e. a perfect hash function). Therefore, the lookup cost is guaranteed to be constant in the worst-case.

Although each second-level table requires quadratic space, if the keys inserted into the first-level hash table are uniformly distributed, the structure as a whole occupies expected O(n) space, since bucket sizes are small with high probability.

If a collision occurs during the insertion of a new entry, the bucket's second-level table is rebuilt with a different randomly-selected hash function. Because the load factor of the second-level table is kept low (1/k), rebuilding is infrequent, and the amortized cost of insertions is low.

External links

Fredman, M. L., Komlós, J., and Szemerédi, E. 1984. Storing a Sparse Table with 0(1) Worst Case Access Time. J. ACM 31, 3 (Jun. 1984), 538-544

Dietzfelbinger, M., Karlin, A., Mehlhorn, K., Meyer auf der Heide, F., Rohnert, H., and Tarjan, R. E. 1994. Dynamic Perfect Hashing: Upper and Lower Bounds. SIAM J. Comput. 23, 4 (Aug. 1994), 738-761.

Dietzfelbinger, M., Hühne, M., and Weidling, C. 2008. A dictionary implementation based on dynamic perfect hashing. J. Exp. Algorithmics 12 (Jun. 2008), 1-25