Related papers: Sampling Colorings and Independent Sets of Random …
Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the…
We propose a deterministic algorithm for approximately counting the number of list colorings of a graph. Under the assumption that the graph is triangle free, the size of every list is at least $\alpha \Delta$, where $\alpha$ is an…
We present a simple combinatorial framework for establishing approximate tensorization of variance and entropy in the setting of spin systems (a.k.a. undirected graphical models) based on balanced separators of the underlying graph. Such…
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…
We consider the problem of distributed lossless computation of a function of two sources by one common user. To do so, we first build a bipartite graph, where two disjoint parts denote the individual source outcomes. We then project the…
We study algorithmic applications of a natural discretization for the hard-sphere model and the Widom-Rowlinson model in a region $\mathbb{V}\subset\mathbb{R}^d$. These models are used in statistical physics to describe mixtures of one or…
For general antiferromagnetic 2-spin systems, including the hardcore model and the antiferromagnetic Ising model, there is an $\mathsf{FPTAS}$ for the partition function on graphs of maximum degree $\Delta$ when the infinite regular tree…
Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
We consider sampling in the so-called low-temperature regime, which is typically characterised by non-local behaviour and strong global correlations. Canonical examples include sampling independent sets on bipartite graphs and sampling from…
We revisit the classical problem of finding an approximately stationary point of the average of $n$ smooth and possibly nonconvex functions. The optimal complexity of stochastic first-order methods in terms of the number of gradient…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
Let $\Delta,q\geq 3$ be integers. We prove that there exists $\eta\geq 0.002$ such that if $q\geq (2-\eta)\Delta$, then there exists an open set $\mathcal{U}\subset \mathbb{C}$ that contains the interval $[0,1]$ such that for each $w\in…
This paper studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $n^{1-\epsilon}$ for any $\epsilon > 0$, is NP-hard in static…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
We consider the $q$-state Potts model on families of self-dual strip graphs $G_D$ of the square lattice of width $L_y$ and arbitrarily great length $L_x$, with periodic longitudinal boundary conditions. The general partition function $Z$…
Citizen science monitoring programs can generate large amounts of valuable data, but are often affected by sampling bias. We focus on a citizen science initiative that records plant-pollinator interactions, with the goal of learning…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity $\l$, where the weight of an independent set $I$ is $\l^{|I|}$. A recent result has established that Gibbs…