A combinatorial analysis of the average time for open-address hash coding insertion

TL;DR

This paper provides a combinatorial analysis of the average insertion time in open-address hash coding, deriving known results through a new combinatorial approach related to musical chairs.

Contribution

It introduces a purely combinatorial method to derive the average insertion time for a hash-coding variant, offering an alternative to previous analytical techniques.

Findings

Derived the exact average number of rejections in the hash-coding process

Connected hash insertion analysis to a musical chairs variant

Validated the combinatorial approach against known expressions

Abstract

In analysing a well-known hash-coding method, Knuth gave an exact expression for the average number of rejections encountered by players of a variant of musical chairs. We study a variant more closely related to musical chairs itself and deduce the same expression by a purely combinatorial approach.