# Parallel Computation of Alpha Complex for Biomolecules

## TL;DR

This paper introduces a GPU-based parallel algorithm for computing the alpha complex of biomolecules, significantly improving performance by up to 50 times over existing methods without needing prior Delaunay triangulation.

## Contribution

The novel algorithm computes the alpha complex directly from biomolecular data using a two-stage process, bypassing the need for Delaunay triangulation and leveraging biomolecular spatial properties.

## Key findings

- Up to 50x speedup compared to existing methods
- Effective in handling various biomolecular structures
- Eliminates the need for prior Delaunay triangulation

## 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.