相关论文: Systematic scan for sampling colorings

This paper is concerned with sampling from the uniform distribution on H-colourings of the n-vertex path using systematic scan Markov chains. An H-colouring of the n-vertex path is a homomorphism from the n-vertex path to some fixed graph…

We study the mixing time of a systematic scan Markov chain for sampling from the uniform distribution on proper 7-colourings of a finite rectangular sub-grid of the infinite square lattice, the grid. A systematic scan Markov chain cycles…

We study the mixing time of systematic scan Markov chains on finite spin systems. It is known that, in a single site setting, the mixing time of systematic scan can be bounded in terms of the influences sites have on each other. We…

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the…

We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the…

For Markov chain Monte Carlo methods, one of the greatest discrepancies between theory and system is the scan order - while most theoretical development on the mixing time analysis deals with random updates, real-world systems are…

In this paper we consider the algorithmic problem of sampling from the Potts model and computing its partition function at low temperatures. Instead of directly working with spin configurations, we consider the equivalent problem of…

Sampling graph colorings via local Markov chains is a central problem in approximate counting and Markov chain Monte Carlo (MCMC). We address the problem of sampling a random $k$-coloring of a graph with maximum degree $\Delta$. The…

We study the problem of approximately counting the number of list packings of a graph. The analogous problem for usual vertex coloring and list coloring has attracted a lot of attention. For list packing the setup is similar but we seek a…

We study the sampling problem for simultaneous edge colorings. Given a pair of graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ which are on the same vertex set $V$, a simultaneous edge coloring is an edge coloring of $G_1\cup G_2$ so that each of…

A popular method for sampling from high-dimensional distributions is the \emph{Gibbs sampler}, which iteratively resamples sites from the conditional distribution of the desired measure given the values of the other coordinates. It is…

We consider the problem of sampling a proper $k$-coloring of a graph of maximal degree $\Delta$ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of bounded treewidth if…

We study Markov chains for randomly sampling $k$-colorings of a graph with maximum degree $\Delta$. Our main result is a polynomial upper bound on the mixing time of the single-site update chain known as the Glauber dynamics for planar…

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 a sparse random graph G(n,d/n), where k=k(d) is a sufficiently…

The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…

We give a new method for analysing the mixing time of a Markov chain using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes…

The goal of this Random Walks project is to code and experiment the Markov Chain Monte Carlo (MCMC) method for the problem of graph coloring. In this report, we present the plots of cost function \(\mathbf{H}\) by varying the parameters…

Gibbs sampling also known as Glauber dynamics is a popular technique for sampling high dimensional distributions defined on graphs. Of special interest is the behavior of Gibbs sampling on the Erd\H{o}s-R\'enyi random graph G(n,d/n). While…

The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…

The property of spatial mixing and strong spatial mixing in spin systems has been of interest because of its implications on uniqueness of Gibbs measures on infinite graphs and efficient approximation of counting problems that are otherwise…