Related papers: Counting without sampling. New algorithms for enum…
Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise,…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…
Sampling from combinatorial families can be difficult. However, complicated families can often be embedded within larger, simpler ones, for which easy sampling algorithms are known. We take advantage of such a relationship to describe a…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
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…
We show that spin systems with bounded degrees and coupling independence admit fully polynomial time approximation schemes (FPTAS). We design a new recursive deterministic counting algorithm to achieve this. As applications, we give the…
An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be…
The following learning problem arises naturally in various applications: Given a finite sample from a categorical or count time series, can we learn a function of the sample that (nearly) maximizes the probability of correctly guessing the…
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…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
Approximate Graph Pattern Mining (AGPM) is essential for analyzing large-scale graphs where exact counting is computationally prohibitive. While there exist numerous sampling-based AGPM systems, they all rely on uniform sampling and…
In this paper, we design efficient algorithms to approximately count the number of edges of a given $k$-hypergraph, and to sample an approximately uniform random edge. The hypergraph is not given explicitly, and can be accessed only through…
In this paper we introduce a new approach for approximately counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula $\Phi$ when the…
We consider two classes of natural stochastic processes on finite unlabeled graphs. These are Euclidean stochastic optimization algorithms on the adjacency matrix of weighted graphs and a modified version of the Metropolis MCMC algorithm on…
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…
The Max-Cut problem is a well known combinatorial optimization problem. In this paper we describe a fast approximation method. Given a graph G, we want to find a cut whose size is maximal among all possible cuts. A cut is a partition of the…
We study the problem of estimating the number of triangles in a graph stream. No streaming algorithm can get sublinear space on all graphs, so methods in this area bound the space in terms of parameters of the input graph such as the…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
An important problem arising in the study of complex networks, for instance in community detection and motif finding, is the sampling of graphs with fixed degree sequence. The equivalent problem of generating random 0,1 matrices with fixed…