Random sampling of colourings of sparse random graphs with a constant number of colours
نویسندگان
چکیده
منابع مشابه
Random sampling of colourings of sparse random graphs with a constant number of colours
In this work we present a simple and efficient algorithm which, with high probability, provides an almost uniform sample from the set of proper k-colourings on an instance of sparse random graphs Gn,d/n, where k = k(d) is a sufficiently large constant. Our algorithm is not based on the Markov Chain Monte Carlo method (M.C.M.C.). Instead, we provide a novel proof of correctness of our Algorithm ...
متن کاملRandomly Colouring Sparse Random Graphs using a Constant number of colours
In this work we present an efficient algorithm which, with high probability, provides an almost uniform sample from the set of proper χ-colourings of an instance of sparse random graphs Gn,d/n, where χ = χ(d) is a sufficiently large constant. This work improves, asymptotically, the result of Dyer, Flaxman Frieze and Vigoda in [4] where the algorithm proposed there needs at least Θ( log log n lo...
متن کاملSampling Random Colorings of Sparse Random Graphs
We study the mixing properties of the single-site Markov chain known as the Glauber dynam-ics for sampling k-colorings of a sparse random graph G(n, d/n) for constant d. The best knownrapid mixing results for general graphs are in terms of the maximum degree ∆ of the input graphG and hold when k > 11∆/6 for all G. Improved results hold when k > α∆ for graphs withgirth ≥ 5 and ∆ ...
متن کاملRandom Sampling of 3-colourings in Z *
We consider the problem of uniformly sampling proper 3-colourings of an m × n rectangular region of Z. We show that the single-site “Glauber-dynamics” Markov chain is rapidly mixing. Our result complements an earlier result of Luby, Randall and Sinclair, which demonstrates rapid mixing when there is a fixed boundary (whose colour cannot be changed). c © John Wiley & Sons, Inc.
متن کاملSampling Grid Colourings with Fewer Colours
We provide an optimally mixing Markov chain for 6-colourings of the square grid. Furthermore, this implies that the uniform distribution on the set of such colourings has strong spatial mixing. 4 and 5 are now the only remaining values of k for which it is not known whether there exists a rapidly mixing Markov chain for k-colourings of the square grid.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2008
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2008.05.008