Very rapid mixing of the Glauber dynamics for proper colorings on bounded-degree graphs
نویسندگان
چکیده
Recent results have shown that the Glauber dynamics for graph colourings has optimal mixing time when (i) the graph is triangle-free and D-regular and the number of colours k is a small constant fraction smaller than 2D, or (ii) the graph has maximum degree D and k = 2D. We extend both these results to prove that the Glauber dynamics has optimal mixing time when the graph has maximum degree D and the number of colours is a small constant fraction smaller than 2D.
منابع مشابه
Subset Glauber Dynamics on Graphs, Hypergraphs and Matroids of Bounded Tree-Width
Motivated by the ‘subgraphs world’ view of the ferromagnetic Ising model, we analyse the mixing times of Glauber dynamics based on subset expansion expressions for classes of graph, hypergraph and matroid polynomials. With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs, hypergraphs and matroids of bounded tree-width. This extends...
متن کاملJu l 2 00 5 A general lower bound for mixing of single - site dynamics on graphs ∗
We prove that any Markov chain that performs local, reversible updates on randomly chosen vertices of a bounded-degree graph necessarily has mixing time at least Ω(n logn), where n is the number of vertices. Our bound applies to the so-called “Glauber dynamics” that has been used extensively in algorithms for the Ising model, independent sets, graph colorings and other structures in computer sc...
متن کاملMatrix norms and rapid mixing for spin systems
We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the associated dependency matrix is less than 1. We give improved analysis for the case in which the diagonal of the dependency matrix is 0 (as in heat bath dynamics...
متن کاملSpatial Mixing of Coloring Random Graphs
We study the strong spatial mixing (decay of correlation) property of proper q-colorings of random graphG(n, d/n) with a fixed d. The strong spatial mixing of coloring and related models have been extensively studied on graphs with bounded maximum degree. However, for typical classes of graphs with bounded average degree, such as G(n, d/n), an easy counterexample shows that colorings do not exh...
متن کاملLocal uniformity properties for glauber dynamics on graph colorings
We investigate some local properties which hold with high probability for randomly selected colorings of a fixed graph with no short cycles. We show that, when the number of colors is sufficiently large relative to the maximum degree of the graph, the aforementioned properties can be used to establish improved bounds on the mixing time for the single-site dynamics, a Markov chain for sampling c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Random Struct. Algorithms
دوره 20 شماره
صفحات -
تاریخ انتشار 2002