FPRAS for the Potts Model and the Number of $k$-colorings
Zonglei Bai, Yongzhi Cao, Hanpin Wang
TL;DR
This paper introduces a Fully Polynomial Randomized Approximation Scheme (FPRAS) for efficiently approximating the partition function of the Potts model and counting the number of k-colorings in graphs, using Markov chain sampling.
Contribution
It presents the first FPRAS for the Potts model and graph k-coloring counting problems based on a novel Markov chain sampling algorithm.
Findings
Developed an efficient sampling algorithm for the Potts model
Provided FPRAS for the Potts model partition function
Provided FPRAS for counting k-colorings
Abstract
In this paper, we give a sampling algorithm for the Potts model using Markov chains. Based on the sampling algorithm, we give \emph{FPRAS}es for the Potts model and the number of -colorings of the graph.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Stochastic processes and statistical mechanics · Bayesian Methods and Mixture Models