Parallel Computation of Alpha Complexes for Biomolecules

Talha Bin Masood, Tathagata Ray and Vijay Natarajan.
Computational Geometry : Theory and Applications, 90, 2020, 1 - 17.
[Elsevier link]
SoCG 2020: Symposium on Computational Geometry 2020, 17:1 - 17:16.

Abstract

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.

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Conference Version

Parallel Computation of Alpha Complexes for Biomolecules
Intl. Symposium on Computational Geometry, 2020, 17:1 - 17:16.

ArXiv version: https://arxiv.org/abs/1908.05944