# 50 years of Linear Probing Hashing

Alfredo Viola (Université de Montevideo, Uruguay)Linear probing hashing is at the core of Analysis of Algorithms by its mathematical and historical interest. This key role is clearly presented in the introduction of a wonderful survey by Flajolet and Chassaing in 2003 oriented to french students, that can be summarized as follows:

“Discrete and continuous mathematics willingly and harmoniously encounter and complement. We would like to illustrate this thesis by presenting a classical problem with several ramifications – the analysis of linear probing hashing. This example is typical of the analysis of algorithms, a topic pioneered by Knuth and which is at the intersection of computer science, combinatorics, and probability theory.”

Historical and scientific motivations include “questions asked by Ramanujan to Hardy in 1913, a summer work in 1962 by Knuth that is at the origin of the analysis of algorithms in computer science, the research in combinatorics done by the statistician Kreweras, several encounters with the model of random graphs by Erdös and Rényi, some complex and asymptotic analysis, trees generated by specific Galton-Watson processes, and, to conclude, a bit of processes like the ineffable Brownian motion!”

All this contributes to a *“very precise understanding of a very simple
discrete random problem”.*

In this talk I will survey the history of linear probing hashing, and present some new work in progress.