Brief Announcement: Unique Permutation Hashing

Abstract

We propose a new open addressing hash function, the unique-permutation hash function, and a performance analysis of its hash computation. A hash function h is simple uniform if items are equally likely to be hashed to any table location (in the first trial). A hash function h is random or strong uniform if the probability of any permutation to be a probe sequence, when using h, is ${{1}\over{N!}}$, where N is the size of the table. We show that the unique-permutation hash function is strong uniform and therefore has the lowest expected cost; each probe sequence is equally likely to be chosen, when the keys are uniformly chosen. Thus, the unique-permutation hash ensures that each empty table location has the same probability to be assigned with a uniformly chosen key.

For constant load factors α< 1, where α is the ratio between the number of inserted items and the table size, the expected time for computing the unique-permutation hash function is O(1) and the expected number of table locations that are checked before an empty location is found, during insertion (or search), is also O(1).

Partially supported by EU ICT-2008-215270 FRONTS, Rita Altura Trust Chair in Computer Sciences, and the Lynne and William Frankel Center for Computer Sciences. See [1] for a detailed version.