Related papers: Dynamic Kernel Graph Sparsifiers
In graph-based data analysis, $k$-nearest neighbor ($k$NN) graphs are widely used due to their adaptivity to local data densities. Allowing weighted edges in the graph, the kernelized graph affinity provides a more general type of $k$NN…
In the fully dynamic maximal matching problem, the goal is to maintain a maximal matching in a graph undergoing an online sequence of edge insertions and deletions. The problem has been studied extensively in the oblivious-adversary…
A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the $d$-dimensional unit sphere, then connecting each pair $(i,j)$ with probability $K(\langle…
A dynamical system of points moving along the edges of a graph could be considered as a geometrical discrete dynamical system or as a discrete version of a quantum graph with localized wave packets. We study the set of such systems over…
We present a data structure that in a dynamic graph of treedepth at most $d$, which is modified over time by edge insertions and deletions, maintains an optimum-height elimination forest. The data structure achieves worst-case update time…
We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…
This work presents inGRASS, a novel algorithm designed for incremental spectral sparsification of large undirected graphs. The proposed inGRASS algorithm is highly scalable and parallel-friendly, having a nearly-linear time complexity for…
We make several advances broadly related to the maintenance of electrical flows in weighted graphs undergoing dynamic resistance updates, including: 1. More efficient dynamic spectral vertex sparsification, achieved by faster length…
Dynamic connectivity is a fundamental dynamic graph problem, and recent algorithmic breakthroughs on dynamic graph sketching have reshaped what is theoretically possible: by encoding the graph as per-vertex linear sketches, these algorithms…
Given a set $A$ of $n$ points (vertices) in general position in the plane, the \emph{complete geometric graph} $K_n[A]$ consists of all $\binom{n}{2}$ segments (edges) between the elements of $A$. It is known that the edge set of every…
This paper considers generalised network, intended as networks where (a) the edges connecting the nodes are nonlinear, and (b) stochastic processes are continuously indexed over both vertices and edges. Such topological structures are…
Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…
While kernel methods and Graph Neural Networks offer complementary strengths, integrating the two has posed challenges in efficiency and scalability. The Graph Neural Tangent Kernel provides a theoretical bridge by interpreting GNNs through…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
Feature selection is an important data preprocessing in data mining and machine learning which can be used to reduce the feature dimension without deteriorating model's performance. Since obtaining annotated data is laborious or even…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
We address the problem of map sparsification for long-term visual localization. For map sparsification, a commonly employed assumption is that the pre-build map and the later captured localization query are consistent. However, this…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…