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Motivated by the problem of compressing point sets into as few bits as possible while maintaining information about approximate distances between points, we construct random nonlinear maps $\varphi_\ell$ that compress point sets in the…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…
The $p$-set, which is in a simple analytic form, is well distributed in unit cubes. The well-known Weil's exponential sum theorem presents an upper bound of the exponential sum over the $p$-set. Based on the result, one shows that the…
Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.…
We describe an exact algorithm for finding the best 2-OPT move which, experimentally, was observed to be much faster than the standard quadratic approach. To analyze its average-case complexity, we introduce a family of heuristic procedures…
Two crucial issues for text summarization to generate faithful summaries are to make use of knowledge beyond text and to make use of cross-sentence relations in text. Intuitive ways for the two issues are Knowledge Graph (KG) and Graph…
We study changes in metrics that are defined on a cartesian product of trees. Such metrics occur naturally in many practical applications, where a global metric (such as revenue) can be broken down along several hierarchical dimensions…
We describe a distributed randomized algorithm computing approximate distances and routes that approximate shortest paths. Let n denote the number of nodes in the graph, and let HD denote the hop diameter of the graph, i.e., the diameter of…
Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of a graph. Some of the most useful graph metrics, especially those measuring social cohesion, are based on…
Motivated by the computational and storage challenges that dense embeddings pose, we introduce the problem of latent network summarization that aims to learn a compact, latent representation of the graph structure with dimensionality that…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
Many systems, including the Internet, social networks, and the power grid, can be represented as graphs. When analyzing graphs, it is often useful to compute scores describing the relative importance or distance between nodes. One example…
Successful applications of deep learning (DL) requires large amount of annotated data. This often restricts the benefits of employing DL to businesses and individuals with large budgets for data-collection and computation. Summarization…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…
Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, the similarity between two trajectories is quantified by means of heuristic…
We consider the following basic problem: given an $n$-variate degree-$d$ homogeneous polynomial $f$ with real coefficients, compute a unit vector $x \in \mathbb{R}^n$ that maximizes $|f(x)|$. Besides its fundamental nature, this problem…
We determine the computational complexity of approximately counting and sampling independent sets of a given size in bounded-degree graphs. That is, we identify a critical density $\alpha_c(\Delta)$ and provide (i) for $\alpha <…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
We describe SynGraphy, a method for visually summarising the structure of large network datasets that works by drawing smaller graphs generated to have similar structural properties to the input graphs. Visualising complex networks is…