Almost random graphs with simple hash functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On Universal Classes of Extremely Random Constant-Time Hash Functions
SIAM Journal on Computing
Tabulation based 4-universal hashing with applications to second moment estimation
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Applications of a Splitting Trick
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Linear Probing with Constant Independence
SIAM Journal on Computing
The power of simple tabulation hashing
Proceedings of the forty-third annual ACM symposium on Theory of computing
Explicit and efficient hash families suffice for cuckoo hashing with a stash
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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A tabulation-based hash function maps a key into multiple derived characters which index random values in tables that are then combined with bitwise exclusive or operations to give the hashed value. Thorup and Zhang [9] presented tabulation-based hash classes that use linear maps over finite fields to map keys of the form (a,b) (composed of two characters, a and b, of equal length) to d derived characters in order to achieve d-wise independence. We present a variant in which d derived characters a+b·i, for i=0,…,d−1 (where arithmetic is over integers) are shown to yield (2d−1)-wise independence. Thus to achieve guaranteed k-wise independence for k≥6, our method reduces by about half the number of probes needed into the tables compared to Thorup and Zhang (they presented a different specialized scheme to give 4-wise [9] and 5-wise [10] independence). Our analysis is based on an algebraic property that characterizes k-wise independence of tabulation-based hashing schemes, and combines this characterization with a geometric argument. We also prove a non-trivial lower bound on the number of derived characters necessary for k-wise independence with our and related hash classes.