2-choice hashing

(data structure)

Definition: A variant of a hash table in which keys are added by hashing with two hash functions. The key is put in the array position with the fewer (colliding) keys. Some collision resolution scheme is needed, unless keys are kept in buckets. The average-case cost of a successful search is O(2 + (m-1)/n), where m is the number of keys and n is the size of the array. The most collisions is log2 ln n + Θ(m/n) with high probability.

Generalization (I am a kind of ...)
hash table.

Aggregate parent (I am a part of or used in ...)

Aggregate child (... is a part of or used in me.)
array, hash function.

See also 2-left hashing.

Note: Called "2-way chaining" in the paper.
Although the average lookup time is similar to a table with a single hash function, the maximum number of collisions is exponentially smaller. This make using buckets or use in real-time systems far more practical. Additional hash functions only decrease the maximum by a constant factor.
Buckets or lists can be searched in parallel.

Michael Mitzenmacher extensively studied and analyzed 2-left and 2-choice hashing.

Author: PEB

More information

Yossi Azar, Andrei Z. Broder, Anna R. Karlin, Eli Upfal, Balanced Allocations, SIAM J. Comput. 29(1):180-200, 1999.
An earlier version appeared in STOC 1994.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 14 August 2008.
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Cite this as:
Paul E. Black, "2-choice hashing", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 14 August 2008. (accessed TODAY) Available from: