Skeletons for distributed topological computation

Abstract

Parallel implementation of topological algorithms is highly desirable, but the challenges, from reconstructing algorithms around independent threads through to runtime load balancing, have proven to be formidable. This problem, made all the more acute by the diversity of hardware platforms, has led to new kinds of implementation platform for computational science, with sophisticated runtime systems managing and coordinating large threadcounts to keep processing elements heavily utilized. While simpler and more portable than direct management of threads, these approaches still entangle program logic with resource management. Similar kinds of highly parallel runtime system have also been developed for functional languages. Here, however, language support for higher-order functions allows a cleaner separation between the algorithm and 'skeletons' that express generic patterns of parallel computation. We report results on using this technique to develop a distributed version of the Joint Contour Net, a generalization of the Contour Tree to multifields. We present performance comparisons against a recent Haskell implementation using shared-memory parallelism, and initial work on a skeleton for distributed memory implementation that utilizes an innovative strategy to reduce inter-process communication overheads.

Visual Identification and Extraction of Intrinsic Axes in High-Dimensional Data

“…Duke et al [43], [44] proposed Joint Contour Net (JCN), a generalization of Reeb graph that allows analysis of multi-field data. Duke and Hosseini [45], Chattopadhyay et al [46] and others proposed corresponding optimization and improvement methods based on JCN. TDA is also suitable for non-functional data, such as Wang et al [47] recovered non-trivial topology structures (such as branches and holes) in high-dimensional data.…”

Topological Visualisation Techniques for Volume Multifield Data

“…Existing development of the algorithm has focused largely on implementation as a parallel algorithm. A distributed memory model is used by Duke and Hosseini [55] to construct multiple sub-JCNs in parallel, these are merged into a single output as a final post-processing step. Current results suggest that the merge step is the limiting factor to parallel algorithm speed up; therefore, other parallelisation strategies are under investigation.…”