TACHYON: Efficient Shared Memory Parallel Computation of Extremum Graphs

The extremum graph is a succinct representation of the Morse decomposition of a scalar field. It has increasingly become a useful data structure that supports topological feature directed visualization of 2D / 3D scalar fields, and enables dimensionality reduction together with exploratory analysis of high dimensional scalar fields. Current methods that employ the extremum graph compute it either using a simple sequential algorithm for computing the Morse decomposition or by computing the more detailed Morse-Smale complex. Both approaches are typically limited to two and three dimensional scalar fields. We describe a GPU-CPU hybrid parallel algorithm for computing the extremum graph of scalar fields in all dimensions. The proposed shared memory algorithm utilizes both fine grained parallelism and task parallelism to achieve efficiency. An open source software library, TACHYON, that implements the algorithm exhibits superior performance and good scaling behavior.