Abstract
It has been shown by various researchers that designing a perfect hashing function for a fixed set ofn elements requires Θ(n) bits in the worst case. A possible relaxation of this scheme is to partition the set into pages, and design a hash function which maps keys to page addresses, requiring subsequent binary search of the page. We have shown elsewhere that (nk/2k+1)(1 +o(1)) bits are necessary and sufficient to describe such a hash function where the pages are of size 2k. In this paper we examine the additional scheme of expanding the address space of the table, which does substantially improve the hash function complexity of perfect hashing, and show that in contrast, it does not reduce the hash function complexity of the paging scheme.
Similar content being viewed by others
References
Berman, Francine, Mary Ellen Bock, Eric Dittert, Michael J. O'Donnell and Darrell Plank.Collections of Functions for Perfect Hashing. Preprint, Purdue University, July 1982.
Fredman, Michael L., János Komlós and Endre Szemerédi.Storing a sparse table with O(1)worst case access time. 23rd IEEE Symposium on Foundations of Computer Science, November 1982, pp. 165–169.
Mairson, Harry G.The program complexity of searching a table. 24th IEEE Symposium on Foundations of Computer Science, November 1983, pp. 40–48.
Mairson, Harry G.The program complexity of searching a table. (Ph.D. thesis) Technical Report STAN-CS-83-988, Department of Computer Science, Stanford University, January 1984.
Marshall, Albert W. and Ingram Olkin.Inequalities: Theory of Majorization and its Applications. New York: Academic Press, 1979.
Mehlhorn, Kurt.On the program size of perfect and universal hashfunctions. 23rd IEEE Symposium on Foundations of Computer Science, November 1982, pp. 170–175.
Author information
Authors and Affiliations
Additional information
Research supported by NSF Grant CCR-9017125 and by a grant from Texas Instruments.