License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.47
URN: urn:nbn:de:0030-drops-66706
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6670/
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Yin, Yitong ; Zhang, Chihao

Sampling in Potts Model on Sparse Random Graphs

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Abstract

We study the problem of sampling almost uniform proper q-colorings in sparse Erdos-Renyi random graphs G(n,d/n), a research initiated by Dyer, Flaxman, Frieze and Vigoda [Dyer et al., RANDOM STRUCT ALGOR, 2006]. We obtain a fully polynomial time almost uniform sampler (FPAUS) for the problem provided q>3d+4, improving the current best bound q>5.5d [Efthymiou, SODA, 2014].

Our sampling algorithm works for more generalized models and broader family of sparse graphs. It is an efficient sampler (in the same sense of FPAUS) for anti-ferromagnetic Potts model with activity 0<=b<1 on G(n,d/n) provided q>3(1-b)d+4. We further identify a family of sparse graphs to which all these results can be extended. This family of graphs is characterized by the notion of contraction function, which is a new measure of the average degree in graphs.

BibTeX - Entry

@InProceedings{yin_et_al:LIPIcs:2016:6670,
  author =	{Yitong Yin and Chihao Zhang},
  title =	{{Sampling in Potts Model on Sparse Random Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{47:1--47:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Klaus Jansen and Claire Mathieu and Jos{\'e} D. P. Rolim and Chris Umans},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6670},
  URN =		{urn:nbn:de:0030-drops-66706},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.47},
  annote =	{Keywords: Potts model, Sampling, Random Graph, Approximation Algorithm}
}

Keywords: Potts model, Sampling, Random Graph, Approximation Algorithm
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)
Issue Date: 2016
Date of publication: 06.09.2016

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