Almost random graphs with simple hash functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Linear probing with constant independence
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
String hashing for linear probing
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On the k-independence required by linear probing and minwise independence
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Linear Probing with 5-wise Independence
SIAM Review
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Universal hash functions that exhibit (c log n)-wise independence are shown to give a performance in double hashing, uniform hashing and virtually anyreasonable generalization of double hashing that has an expected probe count of 1/(1-alpha)+O(1/n) for the insertion of the (alpha n)-th item into a table of size n, for any fixed alpha 1. This performance is optimal. These results are derived from a novel formulation that overestimates the expected probe count by underestimating the presence of local items already inserted into the hash table, and from a very sharp analysis of the underlying stochasticstructures formed by colliding items. Analogous bounds are attained for the expected r-th moment of the probe count, or any fixed r, and linear probing is also shown to achieve a performance with universal hash functions that is equivalent to the fully random case.