# Quadratic exact-size and linear approximate-size random generation of planar graphs

1 ALGORITHMS - Algorithms
Inria Paris-Rocquencourt
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 $\mathcal{O}(n^7)$.
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Type de document :
Communication dans un congrès
Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.125-138, 2005, DMTCS Proceedings
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https://hal.inria.fr/hal-01184034
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Soumis le : mercredi 12 août 2015 - 15:52:02
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
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Eric Fusy. Quadratic exact-size and linear approximate-size random generation of planar graphs. Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.125-138, 2005, DMTCS Proceedings. 〈hal-01184034〉

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