An Analysis of Random-Walk Cuckoo Hashing

Authors:
Alan Frieze;Páll Melsted;Michael Mitzenmacher
Affiliations:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, U.S.A. 15213;Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, U.S.A. 15213;School of Engineering and Applied Sciences, Harvard University, Cambridge 02138
Venue:
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2009

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Abstract

In this paper, we provide a polylogarithmic bound that holds with high probability on the insertion time for cuckoo hashing under the random-walk insertion method. Cuckoo hashing provides a useful methodology for building practical, high-performance hash tables. The essential idea of cuckoo hashing is to combine the power of schemes that allow multiple hash locations for an item with the power to dynamically change the location of an item among its possible locations. Previous work on the case where the number of choices is larger than two has required a breadth-first search analysis, which is both inefficient in practice and currently has only a polynomial high probability upper bound on the insertion time. Here we significantly advance the state of the art by proving a polylogarithmic bound on the more efficient random-walk method, where items repeatedly kick out random blocking items until a free location for an item is found.