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Mapping and localization are crucial problems in robotics and autonomous driving. Recent advances in 3D Gaussian Splatting (3DGS) have enabled precise 3D mapping and scene understanding by rendering photo-realistic images. However, existing…
This paper presents a guidance algorithm for solving the problem of following parametric paths, as well as a curvature-varying speed setpoint for land-based car-type wheeled mobile robots (WMRs). The guidance algorithm relies on…
Current Graph Neural Networks (GNN) architectures generally rely on two important components: node features embedding through message passing, and aggregation with a specialized form of pooling. The structural (or topological) information…
Globally consistent dense maps are a key requirement for long-term robot navigation in complex environments. While previous works have addressed the challenges of dense mapping and global consistency, most require more computational…
Most of the existing robotic exploration schemes use occupancy grid representations and geometric targets known as frontiers. The occupancy grid representation relies on the assumption of independence between grid cells and ignores…
We study the mixing time of random graphs in the $d$-dimensional toric unit cube $[0,1]^d$ generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a…
Graph coarsening aims to reduce the size of a large graph while preserving some of its key properties, which has been used in many applications to reduce computational load and memory footprint. For instance, in graph machine learning,…
Predicting edge weights on graphs has various applications, from transportation systems to social networks. This paper describes a Graph Neural Network (GNN) approach for edge weight prediction with guaranteed coverage. We leverage…
The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\mu : P \to \mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\tau : P \times…
We consider the problem of dominating set-based virtual backbone used for routing in asymmetric wireless ad-hoc networks. These networks have non-uniform transmission ranges and are modeled using the well-established disk graphs. The…
Graph convolutional networks (GCNs) suffer from the irregularity of graphs, while more widely-used convolutional neural networks (CNNs) benefit from regular grids. To bridge the gap between GCN and CNN, in contrast to previous works on…
Comparing two geometric graphs embedded in space is important in the field of transportation network analysis. Given street maps of the same city collected from different sources, researchers often need to know how and where they differ.…
This paper presents a spectral framework for quantifying the differentiation between graph data samples by introducing a novel metric named Graph Geodesic Distance (GGD). For two different graphs with the same number of nodes, our framework…
The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1…
Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications.…
We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
We describe an efficient method for drawing any n-vertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
The inherent connectivity and dependency of graph-structured data, combined with its unique topology-driven access patterns, pose fundamental challenges to conventional data replication and request routing strategies in geo-distributed…