A complexity theory of efficient parallel algorithms
Theoretical Computer Science - Special issue: Fifteenth international colloquium on automata, languages and programming, Tampere, Finland, July 1988
The analysis of closed hashing under limited randomness
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The amazing power of pairwise independence (abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Closed Hashing is Computable and Optimally Randomizable with Universal Hash Functions
Closed Hashing is Computable and Optimally Randomizable with Universal Hash Functions
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
Journal of Algorithms
Strongly History-Independent Hashing with Applications
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
String hashing for linear probing
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Linear Probing with Constant Independence
SIAM Journal on Computing
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
Balanced allocation and dictionaries with tightly packed constant size bins
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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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 access to a hash function with random and independent function values. Carter and Wegman, in their seminal paper on universal hashing, raised the question of extending their analysis to linear probing. However, we show in this paper that linear probing using a 2-wise independent hash function may have expected logarithmic cost per operation. Recently, Paˇtraşcu and Thorup have shown that 3- and 4-wise independent hash functions may also give rise to logarithmic expected query time. 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 hashing with linear probing.