Randomly coloring sparse random graphs with fewer colors than the maximum degree

M Dyer, AD Flaxman, AM Frieze… - Random Structures & …, 2006 - Wiley Online Library
We analyze Markov chains for generating a random k‐coloring of a random graph Gn, d/n.
When the average degree d is constant, a random graph has maximum degree Θ (log n/log …

[PDF][PDF] A survey on the use of Markov chains to randomly sample colourings

A Frieze, E Vigoda - Oxford Lecture Series in Mathematics and its …, 2007 - math.cmu.edu
In recent years there has been considerable progress on the analysis of Markov chains for
generating a random coloring of an input graph. These improvements have come in …

A survey of tool use in modeling education

LTW Agner, TC Lethbridge - 2017 ACM/IEEE 20th International …, 2017 - ieeexplore.ieee.org
We present the results of a survey of tool use in software modeling education conducted
from December 2016 to March 2017. The survey was conducted among 150 professors who …

A deterministic algorithm for counting colorings with 2-Delta colors

J Liu, A Sinclair, P Srivastava - 2019 IEEE 60th Annual …, 2019 - ieeexplore.ieee.org
We give a polynomial time deterministic approximation algorithm (an FPTAS) for counting
the number of q-colorings of a graph of maximum degree Delta, provided only that q≥ …

Coupling with the stationary distribution and improved sampling for colorings and independent sets

TP Hayes, E Vigoda - 2006 - projecteuclid.org
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 …

Improved mixing condition on the grid for counting and sampling independent sets

R Restrepo, J Shin, P Tetali, E Vigoda… - Probability Theory and …, 2013 - Springer
The hard-core model has received much attention in the past couple of decades as a lattice
gas model with hard constraints in statistical physics, a multicast model of calls in …

Randomly coloring constant degree graphs

M Dyer, A Frieze, TP Hayes… - Random Structures & …, 2013 - Wiley Online Library
We study a simple Markov chain, known as the Glauber dynamics, for generating a random
k‐coloring of an n‐vertex graph with maximum degree Δ. We prove that, for every ε> 0, the …

Rapid mixing of Gibbs sampling on graphs that are sparse on average

E Mossel, A Sly - Random Structures & Algorithms, 2009 - Wiley Online Library
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 …

Gibbs rapidly samples colorings of G(n, d/n)

E Mossel, A Sly - Probability theory and related fields, 2010 - Springer
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 …

Correlation decay and partition function zeros: Algorithms and phase transitions

J Liu, A Sinclair, P Srivastava - SIAM Journal on Computing, 2022 - SIAM
We explore connections between the phenomenon of correlation decay (more precisely,
strong spatial mixing) and the location of Lee--Yang and Fisher zeros for various spin …