Tabulation-Based 5-Independent Hashing with Applications to Linear Probing and Second Moment Estimation

Appendix for Tabulation Based 4-Universal Hashing with Applications to Second Moment Estimation

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 comp...

Approximately Minwise Independence with Twisted Tabulation

A random hash function h is ε-minwise if for any set S, |S| “ n, and element x P S, Prrhpxq “ minhpSqs “ p1 ̆ εq{n. Minwise hash functions with low bias ε have widespread applications within similarity estimation. Hashing from a universe rus, the twisted tabulation hashing of Pǎtraşcu and Thorup [SODA’13] makes c “ Op1q lookups in tables of size u1{c. Twisted tabulation was invented to get good ...

Linear Probing with 5-wise Independence

Hashing with linear probing dates back to the 1950s, and is among the most studied algorithms for storing (key,value) pairs. In recent years it has become one of the most important hash table organizations since it uses the cache of modern computers very well. Unfortunately, previous analyses rely either on complicated and space consuming hash functions, or on the unrealistic assumption of free...

Practical Hash Functions for Similarity Estimation and Dimensionality Reduction

Hashing is a basic tool for dimensionality reduction employed in several aspects of machine learning. However, the perfomance analysis is often carried out under the abstract assumption that a truly random unit cost hash function is used, without concern for which concrete hash function is employed. The concrete hash function may work fine on sufficiently random input. The question is if they c...