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| HAL : hal-00466411, version 3 |
| arXiv : 1003.4847 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (25-03-2010) | v2 (31-05-2010) | v3 (06-08-2010) |
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| A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings |
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| Andrea Bedini 1Jesper Jacobsen 2 |
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| (23/03/2010) |
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| Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N=100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the exponential running time ~ exp(0.245 N) provided by the hitherto best known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice. |
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| 1 : | Istituto Nazionale di Fisica Nucleare, Sezione di Milano (INFN, Sezione di Milano) |
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INFN |
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| 2 : | Laboratoire de Physique Théorique de l'ENS (LPTENS) |
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CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris |
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| Domaine | : | Physique/Physique mathématique Mathématiques/Physique mathématique Physique/Matière Condensée/Mécanique statistique Mathématiques/Combinatoire Informatique/Complexité |
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| computational complexity – transfer matrix – tree decomposition – chromatic polynomial |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00466411, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00466411 | |
| oai:hal.archives-ouvertes.fr:hal-00466411 | |
| Contributeur : Jesper Jacobsen | |
| Soumis le : Vendredi 6 Août 2010, 15:30:01 | |
| Dernière modification le : Vendredi 6 Août 2010, 16:03:02 | |
