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Load-Balancing for Parallel Delaunay Triangulations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11725)

Abstract

Computing the Delaunay triangulation (DT) of a given point set in \(\mathbb {R}^D\) is one of the fundamental operations in computational geometry. Recently, Funke and Sanders [11] presented a divide-and-conquer DT algorithm that merges two partial triangulations by re-triangulating a small subset of their vertices – the border vertices – and combining the three triangulations efficiently via parallel hash table lookups. The input point division should therefore yield roughly equal-sized partitions for good load-balancing and also result in a small number of border vertices for fast merging. In this paper, we present a novel divide-step based on partitioning the triangulation of a small sample of the input points. In experiments on synthetic and real-world data sets, we achieve nearly perfectly balanced partitions and small border triangulations. This almost cuts running time in half compared to non-data-sensitive division schemes on inputs exhibiting an exploitable underlying structure.

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Notes

  1. 1.

    For a more detailed description of the primitives we refer to the technical report [12].

  2. 2.

    https://git.scc.kit.edu/dfunke/DelaunayTriangulation.

  3. 3.

    CGAL::Exact_predicates_inexact_constructions_kernel.

  4. 4.

    \(\omega (e = (v,w)) = -\log d(v,w)\) width \(d(\cdot )\) denoting the Euclidean distance.

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Acknowledgments

The authors gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG) who partially supported this work under grants SA 933/10-2 and SA 933/11-1.

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Funke, D., Sanders, P., Winkler, V. (2019). Load-Balancing for Parallel Delaunay Triangulations. In: Yahyapour, R. (eds) Euro-Par 2019: Parallel Processing. Euro-Par 2019. Lecture Notes in Computer Science(), vol 11725. Springer, Cham. https://doi.org/10.1007/978-3-030-29400-7_12

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  • DOI: https://doi.org/10.1007/978-3-030-29400-7_12

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