Efficient Delaunay Tessellation through KD Tree Decomposition
Abstract
Delaunay tessellations are fundamental data structures in computational geometry. They are important in data analysis, where they can represent the geometry of a point set or approximate its density. The algorithms for computing these tessellations at scale perform poorly when the input data is unbalanced. We investigate the use of kd trees to evenly distribute points among processes and compare two strategies for picking split points between domain regions. Because resulting point distributions no longer satisfy the assumptions of existing parallel Delaunay algorithms, we develop a new parallel algorithm that adapts to its input and prove its correctness. We evaluate the new algorithm using two latestage cosmology datasets. The new running times are up to 50 times faster using kd tree compared with regular grid decomposition. Moreover, in the unbalanced data sets, decomposing the domain into a kd tree is up to five times faster than decomposing it into a regular grid.
 Authors:
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 Computational Research Division
 OSTI Identifier:
 1375632
 Report Number(s):
 LBNL1007265
ir:1007265
 Resource Type:
 Conference
 Resource Relation:
 Conference: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, Salt Lake City, Utah, 11/13/2016
 Country of Publication:
 United States
 Language:
 English
Citation Formats
Morozov, Dmitriy, and Peterka, Tom. Efficient Delaunay Tessellation through KD Tree Decomposition. United States: N. p., 2017.
Web. doi:10.1109/SC.2016.61.
Morozov, Dmitriy, & Peterka, Tom. Efficient Delaunay Tessellation through KD Tree Decomposition. United States. doi:10.1109/SC.2016.61.
Morozov, Dmitriy, and Peterka, Tom. 2017.
"Efficient Delaunay Tessellation through KD Tree Decomposition". United States.
doi:10.1109/SC.2016.61. https://www.osti.gov/servlets/purl/1375632.
@article{osti_1375632,
title = {Efficient Delaunay Tessellation through KD Tree Decomposition},
author = {Morozov, Dmitriy and Peterka, Tom},
abstractNote = {Delaunay tessellations are fundamental data structures in computational geometry. They are important in data analysis, where they can represent the geometry of a point set or approximate its density. The algorithms for computing these tessellations at scale perform poorly when the input data is unbalanced. We investigate the use of kd trees to evenly distribute points among processes and compare two strategies for picking split points between domain regions. Because resulting point distributions no longer satisfy the assumptions of existing parallel Delaunay algorithms, we develop a new parallel algorithm that adapts to its input and prove its correctness. We evaluate the new algorithm using two latestage cosmology datasets. The new running times are up to 50 times faster using kd tree compared with regular grid decomposition. Moreover, in the unbalanced data sets, decomposing the domain into a kd tree is up to five times faster than decomposing it into a regular grid.},
doi = {10.1109/SC.2016.61},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 8
}

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