Quadratic Probing Insertions Are $ε^{-(1+o(1))}$

2026-08-28

AI Summary

本文解决了关于二次探测哈希表在负载因子1-ε下的预期插入时间复杂度问题，证明了其为ε^-(1+o(1))，从而确定了该数据结构的复杂性。

Abstract

First proposed in 1968, quadratic probing has stood for more than half a century as one of the simplest and most widely used hash-table designs in computer science. It is conjectured that, at load factor $1 - ε$, the hash table achieves $O(ε^{-1})$ expected insertion time. But even proving a bound of the form $f(ε^{-1})$ for any function $f$ has remained open. In this paper, we prove that the expected insertion time is $ε^{-(1 + o(1))}$. This settles the complexity of the data structure up to sub-polynomial factors in $ε^{-1}$.

Problem

• quadratic probing
• hash table
• insertion time
• load factor
• expected complexity

Innovation

• Quadratic Probing
• Insertion Time
• Complexity Analysis
• Load Factor