Efficient Delaunay Tessellation through K-D Tree Decomposition

Conference · Mon Aug 21 04:00:00 EDT 2017

DOI:https://doi.org/10.1109/SC.2016.61· OSTI ID:1375632

Morozov, Dmitriy; Peterka, Tom

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 k-d 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 late-stage cosmology datasets. The new running times are up to 50 times faster using k-d tree compared with regular grid decomposition. Moreover, in the unbalanced data sets, decomposing the domain into a k-d tree is up to five times faster than decomposing it into a regular grid.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: Computational Research Division
• OSTI ID: 1375632
• Report Number(s): LBNL-1007265; ir:1007265
• Country of Publication: United States
• Language: English