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.

翻译：极值图是标量场Morse分解的简洁表示。它已成为一种日益有用的数据结构，支持2D/3D标量场的拓扑特征导向可视化，并实现高维标量场的降维及探索性分析。当前使用极值图的方法要么采用简单的顺序算法计算Morse分解，要么通过计算更详细的Morse-Smale复形来实现。这两种方法通常局限于二维和三维标量场。我们提出一种GPU-CPU混合并行算法，用于计算任意维度的标量场极值图。该共享内存算法结合了细粒度并行性与任务并行性以实现高效性。实现该算法的开源软件库TACHYON展现出卓越的性能和良好的扩展行为。