Computing the Delaunay triangulation (DT) of a given point set in 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.
CITATION STYLE
Funke, D., Sanders, P., & Winkler, V. (2019). Load-Balancing for Parallel Delaunay Triangulations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11725 LNCS, pp. 156–169). Springer. https://doi.org/10.1007/978-3-030-29400-7_12
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