Related papers: Accelerating Graph Similarity Search through Integ…
Graph embedding is the task of representing nodes of a graph in a low-dimensional space and its applications for graph tasks have gained significant traction in academia and industry. The primary difference among the many recently proposed…
$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…
We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph $G(V, E)$ along with a parameter $p \in (0, 1)$ is given in the input. Each edge of $G$ is realized independently with probability $p$.…
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…
Effective Resistance (ER) is a fundamental tool in various graph learning tasks. In this paper, we address the problem of efficiently approximating ER on a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ with $n$ vertices and $m$ edges.…
Node-level graph anomaly detection (GAD) plays a critical role in identifying anomalous nodes from graph-structured data in various domains such as medicine, social networks, and e-commerce. However, challenges have arisen due to the…
Consider a linear regression model where the design matrix X has n rows and p columns. We assume (a) p is much large than n, (b) the coefficient vector beta is sparse in the sense that only a small fraction of its coordinates is nonzero,…
We propose a new framework for designing test and query functions for complex structures that vary across a given parameter such as genetic marker position. The operations we are interested in include equality testing, set operations,…
Graph similarity search has received considerable attention in many applications, such as bioinformatics, data mining, pattern recognition, and social networks. Existing methods for this problem have limited scalability because of the huge…
In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all…
The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives a proof that, for graphs where each…
Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…
Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…
An identifying code is a subset of vertices of a graph such that each vertex is uniquely determined by its neighbourhood within the identifying code. If $\M(G)$ denotes the minimum size of an identifying code of a graph $G$, it was…
For a hereditary graph class $\mathcal{H}$, the $\mathcal{H}$-elimination distance of a graph $G$ is the minimum number of rounds needed to reduce $G$ to a member of $\mathcal{H}$ by removing one vertex from each connected component in each…
We show that if the degree sequence of a graph $G$ is close in $\ell_1$-distance to a given realizable degree sequence $(d_1,\dots,d_n)$, then $G$ is close in edit distance to a graph with degree sequence $(d_1,\dots,d_n)$. We then use this…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges…
Graph anomaly detection (GAD) is a vital task in graph-based machine learning and has been widely applied in many real-world applications. The primary goal of GAD is to capture anomalous nodes from graph datasets, which evidently deviate…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…