The alpha complex, a subset of the Delaunay triangulation, has been extensively used as the underlying representation for biomolecular structures. We propose a GPU-based parallel algorithm for the computation of the alpha complex, which exploits the knowledge of typical spatial distribution and sizes of atoms in a biomolecule. Unlike existing methods, this algorithm does not require prior construction of the Delaunay triangulation. The algorithm computes the alpha complex in two stages. The first stage proceeds in a bottom-up fashion and computes a superset of the edges, triangles, and tetrahedra belonging to the alpha complex. The false positives from this estimation stage are removed in a subsequent pruning stage to obtain the correct alpha complex. Computational experiments on several biomolecules demonstrate the superior performance of the algorithm, up to a factor of 50 when compared to existing methods that are optimized for biomolecules.

中文翻译：

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生物分子 Alpha 复合物的并行计算

alpha 复合体是 Delaunay 三角剖分的一个子集，已被广泛用作生物分子结构的基础表示。我们提出了一种基于 GPU 的并行算法来计算 alpha 复合物，该算法利用了生物分子中典型空间分布和原子大小的知识。与现有方法不同，该算法不需要事先构建 Delaunay 三角剖分。该算法分两个阶段计算 alpha 复数。第一阶段以自下而上的方式进行，计算属于 alpha 复合体的边、三角形和四面体的超集。来自这个估计阶段的误报在随后的修剪阶段被去除，以获得正确的 alpha 复合体。