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.

α复合物是Delaunay三角剖分的子集，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α复合物，该算法利用了生物分子中典型的空间分布和原子大小的知识。与现有方法不同，此算法不需要事先构造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，并计算属于alpha复合体的边，三角形和四面体的超集。来自此估计阶段的误报在后续的修剪阶段中被删除，以获得正确的alpha复数。