Tabulation Based 5-Universal Hashing and Linear Probing

Previously [SODA'04] we devised the fastest known algorithm for 4-universal hashing. The hashing was based on small pre-computed 4-universal tables. This led to a five-fold improvement in speed over direct methods based on degree 3 polynomials. In this paper, we show that if the pre-computed tables are made 5-universal, then the hash value becomes 5universal without any other change to the computation. Relatively this leads to even bigger gains since the direct methods for 5-universal hashing use degree 4 polynomials. Experimentally, we find that our method can gain up to an order of magnitude in speed over direct 5-universal hashing. Some of the most popular randomized algorithms have been proved to have the desired expected running time using 5-universal hashing, e.g., a non-recursive variant of quicksort takes O(n log n) expected time [Karloff Raghavan JACM'93], and linear probing does updates and searches in O(1) expected time [Pagh et al. SICOMP'09]. In contrast, i...

• Type: Conference
• Year: 2010
• Where: ALENEX
• Authors: Mikkel Thorup, Yin Zhang
• Keywords: 5-universal Hashing, ALENEX 2010, Algorithms, Hashing Scheme, Plain Universal Hashing