Related papers: Edge Nearest Neighbor in Sampling-Based Motion Pla…
Sampling-based methods such as Rapidly-exploring Random Trees (RRTs) have been widely used for generating motion paths for autonomous mobile systems. In this work, we extend time-based RRTs with Control Barrier Functions (CBFs) to generate,…
In nearest-neighbor classification problems, a set of $d$-dimensional training points are given, each with a known classification, and are used to infer unknown classifications of other points by using the same classification as the nearest…
This paper proposes the Real-Time Fast Marching Tree (RT-FMT), a real-time planning algorithm that features local and global path generation, multiple-query planning, and dynamic obstacle avoidance. During the search, RT-FMT quickly looks…
Fixed-radius near neighbor search is a fundamental data operation that retrieves all data points within a user-specified distance to a query point. There are efficient algorithms that can provide fast approximate query responses, but they…
Nearest neighbor (k-NN) graphs are widely used in machine learning and data mining applications, and our aim is to better understand what they reveal about the cluster structure of the unknown underlying distribution of points. Moreover, is…
This work presents a fully integrated tree-based combined exploration-planning algorithm: Exploration-RRT (ERRT). The algorithm is focused on providing real-time solutions for local exploration in a fully unknown and unstructured…
Approximate nearest neighbor (ANN) search is a fundamental problem in many areas of data mining, machine learning and computer vision. The performance of traditional hierarchical structure (tree) based methods decreases as the…
In this paper, we propose a new data structure for approximate nearest neighbor search. This structure augments the neighborhood graph with a bridge graph. We propose to exploit Cartesian concatenation to produce a large set of vectors,…
Sampling-based planning algorithm is a powerful tool for solving planning problems in high-dimensional state spaces. In this article, we present a novel approach to sampling in the most promising regions, which significantly reduces…
Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often…
Path planning has long been an important and active research area in robotics. To address challenges in high-dimensional motion planning, this study introduces the Force Direction Informed Trees (FDIT*), a sampling-based planner designed to…
In this paper we show how the complexity of performing nearest neighbor (NNS) search on a metric space is related to the expansion of the metric space. Given a metric space we look at the graph obtained by connecting every pair of points…
Dynamic graph learning equips the edges with time attributes and allows multiple links between two nodes, which is a crucial technology for understanding evolving data scenarios like traffic prediction and recommendation systems. Existing…
We start with a review of the pervasiveness of the nearest neighbor search problem and techniques used to solve it along with some experimental results. In the second chapter, we show reductions between two different classes of geo- metric…
This paper proposes a sampling based planning algorithm to control autonomous vehicles. We propose an improved Rapidly-exploring Random Tree which includes the definition of K- nearest points and propose a two-stage sampling strategy to…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…
Roadmaps constructed by many sampling-based motion planners coincide, in the absence of obstacles, with standard models of random geometric graphs (RGGs). Those models have been studied for several decades and by now a rich body of…
In the $k$-nearest neighborhood model ($k$-NN), we are given a set of points $P$, and we shall answer queries $q$ by returning the $k$ nearest neighbors of $q$ in $P$ according to some metric. This concept is crucial in many areas of data…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
Many modern methods for prediction leverage nearest neighbor search to find past training examples most similar to a test example, an idea that dates back in text to at least the 11th century and has stood the test of time. This monograph…