On the Insertion Time of Cuckoo Hashing

TL;DR

This paper analyzes the insertion time of cuckoo hashing, demonstrating that under certain conditions, the maximum insertion time is polylogarithmic with high probability, which improves understanding of its efficiency near capacity.

Contribution

It provides a rigorous analysis of the insertion time for cuckoo hashing using a random walk heuristic, especially near the load threshold.

Findings

Maximum insertion time is polylogarithmic with high probability.

Results hold for k > 2 and load close to the threshold.

Enhances theoretical understanding of cuckoo hashing efficiency.

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 further the random walk heuristic for inserting in an online fashion new items into the hash table. Provided that k > 2 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 high probability.