| author: | Éric Fusy |
|---|---|
| title: | Quadratic exact-size and linear approximate-size random generation of planar graphs |
| keywords: | planar graphs, Boltzmann samplers, rejection sampling |
| abstract: |
This extended abstract introduces a new algorithm for the
random generation of labelled planar graphs. Its principles
rely on Boltzmann samplers as recently developed by Duchon,
Flajolet, Louchard, and Schaeffer. It combines the
Boltzmann framework, a judicious use of rejection, a new
combinatorial bijection found by Fusy, Poulalhon and
Schaeffer, as well as a precise analytic description of the
generating functions counting planar graphs, which was
recently obtained by Giménez and Noy. This gives
rise to an extremely efficient algorithm for the random
generation of planar graphs. There is a preprocessing step
of some fixed small cost. Then, for each generation, the
time complexity is quadratic for exact-size uniform
sampling and linear for approximate-size sampling. This
greatly improves on the best previously known time
complexity for exact-size uniform sampling of planar graphs
with
n
vertices, which was a little over
O
(n
7
)
|
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| reference: | Éric Fusy (2005), Quadratic exact-size and linear approximate-size random generation of planar graphs, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 125-138 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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| pdf-source: | dmAD0112.pdf (205 K) |
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