Related papers: Designing Sparse Reliable Pose-Graph SLAM: A Graph…
The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or…
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…
Many modern applications involve accessing and processing graphical data, i.e. data that is naturally indexed by graphs. Examples come from internet graphs, social networks, genomics and proteomics, and other sources. The typically large…
Joint optimization of poses and features has been extensively studied and demonstrated to yield more accurate results in feature-based SLAM problems. However, research on jointly optimizing poses and non-feature-based maps remains limited.…
Recent progress in object pose prediction provides a promising path for robots to build object-level scene representations during navigation. However, as we deploy a robot in novel environments, the out-of-distribution data can degrade the…
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…
In this paper we consider alignment of sparse graphs, for which we introduce the Neighborhood Tree Matching Algorithm (NTMA). For correlated Erd\H{o}s-R\'{e}nyi random graphs, we prove that the algorithm returns -- in polynomial time -- a…
In this paper, we introduce two families of planar and self-similar graphs which have small-world properties. The constructed models are based on an iterative process where each step of a certain formulation of modules results in a final…
We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights, and a subset of edges $E^{\prime} \subset E$ which needs to be removed…
This letter introduces a novel framework for dense Visual Simultaneous Localization and Mapping (VSLAM) based on Gaussian Splatting. Recently, SLAM based on Gaussian Splatting has shown promising results. However, in monocular scenarios,…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
Traditional simultaneous localization and mapping (SLAM) methods focus on improvement in the robot's localization under environment and sensor uncertainty. This paper, however, focuses on mitigating the need for exact localization of a…
Autonomous exploration to build a map of an unknown environment is a fundamental robotics problem. However, the quality of the map directly influences the quality of subsequent robot operation. Instability in a simultaneous localization and…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
Uniform sampling of simple graphs having a given degree sequence is a known problem with exponential complexity in the square of the mean degree. For undirected graphs, randomised approximation algorithms have nonetheless been shown to…
Simultaneous localization and mapping (SLAM) in slowly varying scenes is important for long-term robot task completion. Failing to detect scene changes may lead to inaccurate maps and, ultimately, lost robots. Classical SLAM algorithms…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
The SLAM problem is known to have a special property that when robot orientation is known, estimating the history of robot poses and feature locations can be posed as a standard linear least squares problem. In this work, we develop a SLAM…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
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…