Preprocessing power weighted shortest path data using a s-Well Separated Pair Decomposition

For $s$ $>$ 0, we consider an algorithm that computes all $s$-well separated pairs in certain point sets in $\mathbb{R}^{n}$, $n$ $>1$. For an integer $K$ $>1$, we also consider an algorithm that is a permutation of Dijkstra's algorithm, that computes $K$-nearest neighbors using a cert...

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Bibliographic Details
Main Authors Kalsi, Gurpreet S, Damelin, Steven B
Format Journal Article
LanguageEnglish
Published 20.03.2021
Subjects
Computer Science - Computational Geometry
Computer Science - Computer Vision and Pattern Recognition
Computer Science - Data Structures and Algorithms
Computer Science - Learning
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Summary:For $s$ $>$ 0, we consider an algorithm that computes all $s$-well separated pairs in certain point sets in $\mathbb{R}^{n}$, $n$ $>1$. For an integer $K$ $>1$, we also consider an algorithm that is a permutation of Dijkstra's algorithm, that computes $K$-nearest neighbors using a certain power weighted shortest path metric in $\mathbb{R}^{n}$, $n$ $>$ $1$. We describe each algorithm and their respective dependencies on the input data. We introduce a way to combine both algorithms into a fused algorithm. Several open problems are given for future research.
DOI:10.48550/arxiv.2103.11216