Book ChapterDOI
Geometric minimum spanning trees with GEOFILTERKRUSKAL
Samidh Chatterjee,Michael Connor,Piyush Kumar +2 more
- pp 486-500
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TLDR
The proposed GeoFilterKruskal algorithm, an algorithm that computes the minimum spanning tree of P using well separated pair decomposition in combination with a simple modification of Kruskal’s algorithm, is currently the best practical algorithm on multi-core machines for d>2.Abstract:
Let P be a set of points in ℝd. We propose GeoFilterKruskal, an algorithm that computes the minimum spanning tree of P using well separated pair decomposition in combination with a simple modification of Kruskal’s algorithm. When P is sampled from uniform random distribution, we show that our algorithm takes one parallel sort plus a linear number of additional steps, with high probability, to compute the minimum spanning tree. Experiments show that our algorithm works better in practice for most data distributions compared to the current state of the art [31]. Our algorithm is easy to parallelize and to our knowledge, is currently the best practical algorithm on multi-core machines for d>2.read more
Citations
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Proceedings ArticleDOI
Fast Parallel Algorithms for Euclidean Minimum Spanning Tree and Hierarchical Spatial Clustering
TL;DR: In this article, the authors present new parallel algorithms for generating Euclidean minimum spanning trees and spatial clustering hierarchies (known as HDBSCAN*) based on generating a well-separated pair decomposition followed by using Kruskal's minimum spanning tree algorithm and bichromatic closest pair computations.
Proceedings ArticleDOI
Parallel Cover Trees and their Applications
TL;DR: This paper shows highly parallel and work-efficient cover tree algorithms that can handle batch insertions (and thus construction) and batch deletions and uses three key ideas to guarantee work-efficiency: the prefix-doubling scheme, a careful design to limit the graph size on which it applies MIS, and a strategy to propagate information among different levels in the cover tree.
Journal ArticleDOI
Efficient Retrieval of Top-k Weighted Triangles on Static and Dynamic Spatial Data
TL;DR: This work considers graphs consisting of spatial points, where each point has edges to its nearby points and the weight of each edge is the distance between the corresponding points, and focuses on triangles in such graphs and addresses the problem of retrieving the top-k weighted spatial triangles.
Posted Content
Fast Parallel Algorithms for Euclidean Minimum Spanning Tree and Hierarchical Spatial Clustering
TL;DR: In this paper, a parallel algorithm for minimum spanning trees and spatial clustering hierarchies is presented, which is based on generating a well-separated pair decomposition followed by using Kruskal's minimum spanning tree algorithm and bichromatic closest pair computations.
Experimental approaches to computational geometric and statistical machine translation problems
Piyush Kumar,Samidh Chatterjee +1 more
TL;DR: An algorithm is developed that uses computational geometric tools to find an approximate solution to the 1-Center problem, instantaneously, and succeeds in overcoming this drawback, without compromising in the running time both in theory and in practice.
References
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Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Computational geometry. an introduction
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Journal ArticleDOI
Introduction to algorithms: 4. Turtle graphics
TL;DR: In this article, a language similar to logo is used to draw geometric pictures using this language and programs are developed to draw geometrical pictures using it, which is similar to the one we use in this paper.
Journal ArticleDOI
On the shortest spanning subtree of a graph and the traveling salesman problem
TL;DR: Kurosh and Levitzki as discussed by the authors, on the radical of a general ring and three problems concerning nil rings, Bull Amer Math Soc vol 49 (1943) pp 913-919 10 -, On the structure of algebraic algebras and related rings.