Brief Announcement: Unique Permutation Hashing

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/(N!)]{{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 αα 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).