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$\newcommand{\eps}{\varepsilon}$ 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 problem of learning distance-based Graph Convolutional Networks (GCNs) for relational data. Specifically, we first embed the original graph into the Euclidean space $\mathbb{R}^m$ using a relational density estimation…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…
Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street…
Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. Unsupervised graph embedding methods aim to capture graph structure by learning a…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…
A network embedding is a representation of a large graph in a low-dimensional space, where vertices are modeled as vectors. The objective of a good embedding is to preserve the proximity between vertices in the original graph. This way,…
Greedy navigation/routing plays an important role in geometric routing of networks because of its locality and simplicity. This can operate in geometrically embedded networks in a distributed manner, distances are calculated based on…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
Financial transactions can be considered edges in a heterogeneous graph between entities sending money and entities receiving money. For financial institutions, such a graph is likely large (with millions or billions of edges) while also…
We are given an integer $d$, a graph $G=(V,E)$, and a uniformly random embedding $f : V \rightarrow \{0,1\}^d$ of the vertices. We are interested in the probability that $G$ can be "realized" by a scaled Euclidean norm on $\mathbb{R}^d$, in…
Bidirectional motion planning often reduces planning time compared to its unidirectional counterparts. It requires connecting the forward and reverse search trees to form a continuous path. However, this process could fail and restart the…
In this paper we introduce self-approaching graph drawings. A straight-line drawing of a graph is self-approaching if, for any origin vertex s and any destination vertex t, there is an st-path in the graph such that, for any point q on the…
Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane…
The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…