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
The power of simple tabulation hashing
Proceedings of the forty-third annual ACM symposium on Theory of computing
Linear Probing with 5-wise Independence
SIAM Review
The Power of Simple Tabulation Hashing
Journal of the ACM (JACM)
Independence of tabulation-based hash classes
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
SIAM Journal on Computing
Bottom-k and priority sampling, set similarity and subset sums with minimal independence
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Hashing with linear probing dates back to the 1950s and is among the most widely studied algorithms. In recent years, it has become one of the most important hash table organizations because it uses the cache of modern computers very well. Unfortunately, previous analyses relied either on complicated and space-consuming hash functions, or on the unrealistic assumption of free access to a hash function with random and independent function values. Carter and Wegman, in their seminal paper on universal hashing, have already raised the question of extending their analysis to linear probing. However, we show in this paper that linear probing using a pairwise independent family may have expected logarithmic cost per operation. On the positive side, we show that 5-wise independence is enough to ensure constant expected time per operation. This resolves the question of finding a space- and time-efficient hash function that provably ensures good performance for linear probing.