Modern data collection methods can capture representations of 3D objects at resolutions much greater than they can be discretely rendered as an image. To improve the efficiency of storage, transmission, rendering, and editing of 3D models constructed from such data, it is beneficial to first employ a mesh reduction technique to reduce the size of a mesh. Vertex clustering, a technique that merges close vertices together, has particularly wide applicability, because it operates only on vertices and their spatial proximity. However, it is also very difficult to accelerate with parallelisation in a deterministic manner because it contains extensive algorithmic dependencies.