Related papers: Finding and Counting Patterns in Sparse Graphs
In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple…
We present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of…
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…
We propose Sparse Neural Network architectures that are based on random or structured bipartite graph topologies. Sparse architectures provide compression of the models learned and speed-ups of computations, they can also surpass their…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
We address the problem of computing the distribution of induced connected subgraphs, aka \emph{graphlets} or \emph{motifs}, in large graphs. The current state-of-the-art algorithms estimate the motif counts via uniform sampling, by…
We study the notion of local treewidth in sparse random graphs: the maximum treewidth over all $k$-vertex subgraphs of an $n$-vertex graph. When $k$ is not too large, we give nearly tight bounds for this local treewidth parameter; we also…
Exploring statistics of locally connected subgraph patterns (also known as network motifs) has helped researchers better understand the structure and function of biological and online social networks (OSNs). Nowadays the massive size of…
Given a pattern string $P$ of length $n$ and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet of size $\Delta$, the {\em exact string matching} problem consists of finding all occurrences of…
Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…
We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph $G$, our algorithms output a…
Random walk based distance measures for graphs such as commute-time distance are useful in a variety of graph algorithms, such as clustering, anomaly detection, and creating low dimensional embeddings. Since such measures hinge on the…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
Network motif provides a way to uncover the basic building blocks of most complex networks. This task usually demands high computer processing, specially for motif with 5 or more vertices. This paper presents an extended methodology with…
Learned sparse text embeddings have gained popularity due to their effectiveness in top-k retrieval and inherent interpretability. Their distributional idiosyncrasies, however, have long hindered their use in real-world retrieval systems.…
We study learning problems on correlated stochastic block models with two balanced communities. Our main result gives the first efficient algorithm for graph matching in this setting. In the most interesting regime where the average degree…