Recursive Combinatorial Structures: Enumeration, Probabilistic Analysis and Random Generation

Salvy, Bruno

doi:10.4230/LIPIcs.STACS.2018.1

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LIPIcs.STACS.2018.1.pdf

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DOI: 10.4230/LIPIcs.STACS.2018.1
URN: urn:nbn:de:0030-drops-85352

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Bruno Salvy

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Bruno Salvy. Recursive Combinatorial Structures: Enumeration, Probabilistic Analysis and Random Generation. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 1:1-1:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.STACS.2018.1

Abstract

In a probabilistic context, the main data structures of computer science are viewed as random combinatorial objects. Analytic Combinatorics, as described in the book by Flajolet and Sedgewick, provides a set of high-level tools for their probabilistic analysis. Recursive combinatorial definitions lead to generating function equations from which efficient algorithms can be designed for enumeration, random generation and, to some extent, asymptotic analysis. With a focus on random generation, this tutorial first covers the basics of Analytic Combinatorics and then describes the idea of Boltzmann sampling and its realisation. The tutorial addresses a broad TCS audience and no particular pre-knowledge on analytic combinatorics is expected.

Keywords

Analytic Combinatorics
Generating Functions
Random Generation

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References

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