FoCM 2014 conference

Workshop A4 - Graph Theory and Combinatorics

December 13, 16:00 ~ 16:30 - Room B11

## A unified approach to linear probing hashing

### Universidad de la República, Uruguay   -   viola@fing.edu.uy

We give a unified analysis of linear probing hashing with a general bucket size. We use both a combinatorial approach, giving exact formulas for generating functions, and a probabilistic approach, giving simple derivations of asymptotic results. Both approaches complement nicely, and give a good insight in the relation between linear probing and random walks. The Poisson Transform links in a natural way both approaches. A key methodological contribution, at the core of Analytic Combinatorics, is the use of the symbolic method (based on $q$-calculus) to directly derive the generating functions to analyze.

Joint work with Svante Janson (Uppsala University, Sweden).