Related papers: Sampling Colorings and Independent Sets of Random …
Approximate random $k$-colouring of a graph $G$ is a well studied problem in computer science and statistical physics. It amounts to constructing a $k$-colouring of $G$ which is distributed close to {\em Gibbs distribution} in polynomial…
We study the computational complexity of estimating local observables for Gibbs distributions. A simple combinatorial example is the average size of an independent set in a graph. In a recent work, we established NP-hardness of…
We present a new algorithm for the exact uniform sampling of proper \(k\)-colorings of a graph on \(n\) vertices with maximum degree~\(\Delta\). The algorithm is based on partial rejection sampling (PRS) and introduces a soft relaxation of…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
We examine the problem of almost-uniform sampling proper $q$-colorings of a graph whose maximum degree is $\Delta$. A famous result, discovered independently by Jerrum(1995) and Salas and Sokal(1997), is that, assuming $q > (2+\delta)…
Graph coloring is arguably the most exhaustively studied problem in the area of approximate counting. It is conjectured that there is a fully polynomial-time (randomized) approximation scheme (FPTAS/FPRAS) for counting the number of proper…
We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core…
Recent developments in approximate counting have made startling progress in developing fast algorithmic methods for approximating the number of solutions to constraint satisfaction problems (CSPs) with large arities, using connections to…
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…
A two-state spin system is specified by a 2 x 2 matrix A = {A_{0,0} A_{0,1}, A_{1,0} A_{1,1}} = {\beta 1, 1 \gamma} where \beta, \gamma \ge 0. Given an input graph G=(V,E), the partition function Z_A(G) of a system is defined as Z_A(G) =…
Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006) establish a beautiful picture for the computational complexity of approximating the partition function of the hard-core…
We analyse uniformly random proper $k$-colourings of sparse graphs with maximum degree $\Delta$ in the regime $\Delta < k\ln k $. This regime corresponds to the lower side of the shattering threshold for random graph colouring, a…
We study the computational complexity of approximately counting the number of independent sets of a graph with maximum degree Delta. More generally, for an input graph G=(V,E) and an activity lambda>0, we are interested in the quantity…
Local samplers are algorithms that generate random samples based on local queries to high-dimensional distributions, ensuring the samples follow the correct induced distributions while maintaining time complexity that scales locally with…
Brooks' theorem states that all connected graphs but odd cycles and cliques can be colored with $\Delta$ colors, where $\Delta$ is the maximum degree of the graph. Such colorings have been shown to admit non-trivial distributed algorithms…
We consider the problem of sampling from the Potts model on random regular graphs. It is conjectured that sampling is possible when the temperature of the model is in the uniqueness regime of the regular tree, but positive algorithmic…
We present a randomized algorithm that takes as input an undirected $n$-vertex graph $G$ with maximum degree $\Delta$ and an integer $k > 3\Delta$, and returns a random proper $k$-coloring of $G$. The distribution of the coloring is…
In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial approximation scheme for count- ing exponentially weighted independent sets (equivalently, approximating the partition function of the hard-core model from…
In this paper we study fractional coloring from the angle of distributed computing. Fractional coloring is the linear relaxation of the classical notion of coloring, and has many applications, in particular in scheduling. It was proved by…