Related papers: Counting without sampling. New algorithms for enum…
Sampling from the stationary distribution is one of the fundamental tasks of Markov chain-based algorithms and has important applications in machine learning, combinatorial optimization and network science. For the quantum case, qsampling…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
We consider the problem of sampling and approximately counting an arbitrary given motif $H$ in a graph $G$, where access to $G$ is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…
The maximum independent set problem is a classic optimization problem that has also been studied quite intensively in the distributed setting. While the problem is hard to approximate in general, there are good approximation algorithms…
We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…
Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…
We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…
We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the…
We introduce a Markov Chain Monte Carlo algorithm which samples from the space of spanning trees of complete graphs using local rewiring operations only. The probability distribution of graphs of this kind is shown to depend on the…
Counting the independent sets of a graph is a classical #P-complete problem, even in the bipartite case. We give an exponential-time approximation scheme for this problem which is faster than the best known algorithm for the exact problem.…
Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…
On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…
In this work we introduce a new notion: local mechanisms. These are truthful mechanisms that have an implementation as fast distributed algorithms and non-trivial approximation guarantees. We show how monotone distributed optimisation…
In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to…
Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led…
We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde{O}(n^2)$-time algorithms, where $n$ is the size of the…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…