平行德洛内三角剖分的负载均衡
Load-Balancing for Parallel Delaunay Triangulations
摘要：
在$\mathbb{R}^D$中计算给定点集的德洛内三角剖分（DT）是计算几何的基本运算之一。最近，Funke和Sanders（2017）提出了一种分治DT算法，该算法通过重新三角化顶点的一个小子集（边界顶点）合并两个部分三角形，并通过并行哈希表查找有效地组合三个三角形。因此，输入点划分应该产生大致相等大小的分区，以实现良好的负载均衡，并且还产生少量的边界顶点以实现快速合并。在本文中，我们提出了一种新的划分步骤的基础上划分三角剖分的小样本的输入点。在合成和真实世界的数据集上的实验中，我们实现了几乎完美的平衡分区和小边界三角剖分。这几乎减少了一半的运行时间相比，非数据敏感的划分方案的输入展示了一个可利用的底层结构。
英文摘要：
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 (2017) 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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