相关论文: Systematic scan for sampling colorings
We study the mixing time of systematic scan Glauber dynamics Ising model on the complete graph. On the complete graph $K_n$, at each time, $k \leq n$ vertices are chosen uniformly random and are updated one by one according to the uniformly…
We study the strong spatial mixing (decay of correlation) property of proper $q$-colorings of random graph $G(n, d/n)$ with a fixed $d$. The strong spatial mixing of coloring and related models have been extensively studied on graphs with…
Understanding the local structure of a graph provides valuable insights about the underlying phenomena from which the graph has originated. Sampling and examining k-subgraphs is a widely used approach to understand the local structure of a…
Circular coloring is a constraints satisfaction problem where colors are assigned to nodes in a graph in such a way that every pair of connected nodes has two consecutive colors (the first color being consecutive to the last). We study…
Sampling from Gibbs distribution is a central problem in computer science as well as in statistical physics. In this work we focus on the k-colouring model} and the hard-core model with fugacity \lambda when the underlying graph is an…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained,…
In a previous version of this document we misinterpreted the runtime of a part of the described algorithm. Indeed, the runtime is not better than the Grover-Algorithm. We therefor withdraw this work. We present a novel algorithmic approach…
We study the mixing properties of the single-site Markov chain known as the Glauber dynamics for sampling $k$-colorings of a sparse random graph $G(n,d/n)$ for constant $d$. The best known rapid mixing results for general graphs are in…
The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte-Carlo simulations. We critically discuss…
We study the structure learning problem for $H$-colorings, an important class of Markov random fields that capture key combinatorial structures on graphs, including proper colorings and independent sets, as well as spin systems from…
Sampling from the $q$-state ferromagnetic Potts model is a fundamental question in statistical physics, probability theory, and theoretical computer science. On general graphs, this problem may be computationally hard, and this hardness…
Coloring the vertices of a graph G subject to given conditions can be considered as a random experiment and corresponding to this experiment, a discrete random variable X can be defined as the colour of a vertex chosen at random, with…
We study the dynamics of a backtracking procedure capable of proving uncolourability of graphs, and calculate its average running time T for sparse random graphs, as a function of the average degree c and the number of vertices N. The…
We study a colored generalization of the famous simple-switch Markov chain for sampling the set of graphs with a fixed degree sequence. Here we consider the space of graphs with colored vertices, in which we fix the degree sequence and…
Bounding chains are a technique that offers three benefits to Markov chain practitioners: a theoretical bound on the mixing time of the chain under restricted conditions, experimental bounds on the mixing time of the chain that are provably…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
Mixing of finite time-homogeneous Markov chains is well understood nowadays, with a rich set of techniques to estimate their mixing time. In this paper, we study the mixing time of random walks in dynamic random environments. To that end,…
The problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertex-colored temporal graph, asks for a path whose vertices have…
We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high…