On the Insertion Time of Cuckoo Hashing

Abstract

Cuckoo hashing is an efficient technique for creating large hash tables with high space utilization and guaranteed constant access times. There, each item can be placed in a location given by any one out of $k$ different hash functions. In this paper we investigate the random-walk heuristic for inserting in an online fashion new items into the hash table. Provided that $k \ge 3$ and that the number of items in the table is below (but arbitrarily close to) the theoretically achievable load threshold, we show a polylogarithmic bound for the maximum insertion time that holds with probability $1-o(1)$ as the size of the table grows large.