Two-way Linear Probing Revisited

TL;DR

This paper revisits two-way linear probing hashing schemes, demonstrating that they achieve near-optimal worst-case unsuccessful search times of O(log log n) with high probability, and establishing matching lower bounds.

Contribution

It introduces two-way linear probing schemes with provably optimal worst-case search times and provides matching lower bounds on cluster sizes for such algorithms.

Findings

Achieves O(log log n) worst-case unsuccessful search time

Provides matching lower bounds on cluster sizes

Demonstrates near-optimal performance of two-way linear probing

Abstract

We introduce linear probing hashing schemes that construct a hash table of size $n$, with constant load factor $\alpha$, on which the worst-case unsuccessful search time is asymptotically almost surely $O(\log \log n)$. The schemes employ two linear probe sequences to find empty cells for the keys. Matching lower bounds on the maximum cluster size produced by any algorithm that uses two linear probe sequences are obtained as well.