## Séminaire Algorithmique |

Le séminaire a lieu **le mardi à 11 h 45** (sauf modification exceptionnelle), au campus Côte de Nacre, bâtiment Sciences 3, salle S3 351, 3ème étage.

# Résumé du séminaire du Mardi 25 Juin 2013

*50 years of Linear Probing Hashing*

## par 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.