Related papers: Kinetic $k$-Semi-Yao Graph and its Applications
We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…
Graph Neural Networks (GNNs) have emerged as a promising tool to handle data exhibiting an irregular structure. However, most GNN architectures perform well on homophilic datasets, where the labels of neighboring nodes are likely to be the…
In the task of Knowledge Graph Completion (KGC), the existing datasets and their inherent subtasks carry a wealth of shared knowledge that can be utilized to enhance the representation of knowledge triplets and overall performance. However,…
High-level robotic manipulation tasks demand flexible 6-DoF grasp estimation to serve as a basic function. Previous approaches either directly generate grasps from point-cloud data, suffering from challenges with small objects and sensor…
Land-use monitoring is fundamental for spatial planning, particularly in view of compound impacts of growing global populations and climate change. Despite existing applications of deep learning in land use monitoring, standard…
Knowledge Graphs (KGs) and their machine learning counterpart, Knowledge Graph Embedding Models (KGEMs), have seen ever-increasing use in a wide variety of academic and applied settings. In particular, KGEMs are typically applied to KGs to…
We study the geodesic Voronoi diagram of a set $S$ of $n$ linearly moving sites inside a static simple polygon $P$ with $m$ vertices. We identify all events where the structure of the Voronoi diagram changes, bound the number of such…
Graph Neural Networks have shown excellent performance on semi-supervised classification tasks. However, they assume access to a graph that may not be often available in practice. In the absence of any graph, constructing k-Nearest Neighbor…
In this paper, we utilize a variant of the scaled relative graph (SRG), referred to as the $\theta$-symmetric SRG, to develop a graphical stability criterion for the feedback interconnection of a cascade of systems. A crucial…
The problem of identifying the k-shortest paths (KSPs for short) in a dynamic road network is essential to many location-based services. Road networks are dynamic in the sense that the weights of the edges in the corresponding graph…
k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic…
Graph neural networks (GNN) have shown significant capabilities in handling structured data, yet their application to dynamic, temporal data remains limited. This paper presents a new type of graph attention network, called TempoKGAT, which…
The dissertation is related to combinatorial geometry with a strong probabilistic flavor. The main results can be split into three parts. The results of the first part guarantee that each "unit distance graph" in the plane has an induced…
We study, in three parts, degree sequences of k-families (or k-uniform hypergraphs) and shifted k-families. The first part collects for the first time in one place, various implications such as: Threshold implies Uniquely Realizable implies…
Nearest neighbor search is known as a challenging issue that has been studied for several decades. Recently, this issue becomes more and more imminent in viewing that the big data problem arises from various fields. In this paper, a…
Spectral analysis of neighborhood graphs is one of the most widely used techniques for exploratory data analysis, with applications ranging from machine learning to social sciences. In such applications, it is typical to first encode…
The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between…
The subdivision graph $S(\Sigma)$ of a graph $\Sigma$ is obtained from $\Sigma$ by `adding a vertex' in the middle of every edge of $\Si$. Various symmetry properties of $\S(\Sigma)$ are studied. We prove that, for a connected graph…
K-core decomposition is a commonly used metric to analyze graph structure or study the relative importance of nodes in complex graphs. Recent years have seen rapid growth in the scale of the graph, especially in industrial settings. For…
For a positive integer $k$ and an ordered set of $n$ points in the plane, define its k-sector ordered Yao graphs as follows. Divide the plane around each point into $k$ equal sectors and draw an edge from each point to its closest…