A GPU Parallel Algorithm for Computing Morse-Smale Complexes

TL;DR

This paper introduces a GPU-based parallel algorithm for efficiently computing Morse-Smale complexes, significantly accelerating the process and enabling detailed topological analysis of complex scientific data.

Contribution

It presents a novel fine-grained parallel algorithm and GPU implementation for Morse-Smale complex computation, addressing previous algorithmic challenges.

Findings

Achieves up to 8.6x speedup over pyms3d

Achieves up to 6x speedup over TTK

Provides a CPU-based method for Morse-Smale complex simplification

Abstract

The Morse-Smale complex is a well studied topological structure that represents the gradient flow behavior between critical points of a scalar function. It supports multi-scale topological analysis and visualization of feature-rich scientific data. Several parallel algorithms have been proposed towards the fast computation of the 3D Morse-Smale complex. Its computation continues to pose significant algorithmic challenges. In particular, the non-trivial structure of the connections between the saddle critical points are not amenable to parallel computation. This paper describes a fine grained parallel algorithm for computing the Morse-Smale complex and a GPU implementation gMSC. The algorithm first determines the saddle-saddle reachability via a transformation into a sequence of vector operations, and next computes the paths between saddles by transforming it into a sequence of matrix operations. Computational experiments show that the method achieves up to 8.6x speedup over pyms3d and 6x speedup over TTK, the current shared memory implementations. The paper also presents a comprehensive experimental analysis of different steps of the algorithm and reports on their contribution towards runtime performance. Finally, it introduces a CPU based data parallel algorithm for simplifying the Morse-Smale complex via iterative critical point pair cancellation.