Related papers: Learning Minimally Rigid Graphs with High Realizat…
During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown to work well in practice and to possess theoretical guarantees such as probabilistic…
The 1-median problem (1MP) on undirected weighted graphs seeks to find a facility location minimizing the total weighted distance to all customer nodes. Although the 1MP can be solved exactly by computing the single-source shortest paths…
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…
Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by…
We investigate the Minimum Eccentricity Shortest Path problem in some structured graph classes. It asks for a given graph to find a shortest path with minimum eccentricity. Although it is NP-hard in general graphs, we demonstrate that a…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
Analog quantum computing with Rydberg atoms is seen as an avenue to solve hard graph optimization problems, because they naturally encode the Maximum Independent Set (MIS) problem on Unit-Disk (UD) graphs, a problem that admits rather…
There has been a surge of recent interest in learning representations for graph-structured data. Graph representation learning methods have generally fallen into three main categories, based on the availability of labeled data. The first,…
Graph representation learning (a.k.a. network embedding) is a significant topic of network analysis, due to its effectiveness to support various graph inference tasks. In this paper, we study the representation learning with multiple…
As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…
Computing the edge expansion of a graph is a famously hard combinatorial problem for which there have been many approximation studies. We present two variants of exact algorithms using semidefinite programming (SDP) to compute this constant…
We propose a novel optimization-based approach to embedding heterogeneous high-dimensional data characterized by a graph. The goal is to create a two-dimensional visualization of the graph structure such that edge-crossings are minimized…
Graph Neural Networks (GNNs) have achieved state-of-the-art performance in solving graph classification tasks. However, most GNN architectures aggregate information from all nodes and edges in a graph, regardless of their relevance to the…
The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known…
The \emph{graph realization problem} is to find for given nonnegative integers $a_1,\dots,a_n$ a simple graph (no loops or multiple edges) such that each vertex $v_i$ has degree $a_i.$ Given pairs of nonnegative integers…
The discovery and analysis of network patterns are central to the scientific enterprise. In the present work, we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate…
Graph transformer has been proven as an effective graph learning method for its adoption of attention mechanism that is capable of capturing expressive representations from complex topological and feature information of graphs. Graph…
Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework contracting edges of a graph (merging vertices…
Graph Representation Learning (GRL) has experienced significant progress as a means to extract structural information in a meaningful way for subsequent learning tasks. Current approaches including shallow embeddings and Graph Neural…