Spatiotemporal Domain Decomposition for High Performance Computing: A Flexible Splits Heuristic to Minimize Redundancy

Abstract

There are three steps towards implementing the divide-and-conquer strategy for accelerating spatiotemporal analysis: First, performing spatiotemporal domain decomposition: dividing a large computational task into smaller parts (subdomains) by partitioning the input dataset along its spatiotemporal domain. Second, computing a spatiotemporal analysis algorithm (e.g., kernel density estimation) for each of the resulting subdomains using high performance parallel computing. Third, collecting and reassembling the outputs. However, as many spatiotemporal analysis approaches employ neighborhood search, data elements near domain boundaries need to be assigned to multiple processors by replication to avoid spurious boundary effects. We focus on the first step of the divide-and-conquer strategy because replication of data decreases the efficiency of our approach. We develop a spatiotemporal domain decomposition method (ST-FLEX-D) that allows for flexibility in domain split positions, which refines the well-known static approach (ST-STATIC-D). We design a heuristic to find domain splits that minimize data replication and compare the resulting set of subdomains to ST-STATIC-D using the following metrics: (1) execution time of decomposition, (2) total number of replicated data points, (3) average leaf node depth, and (4) average leaf node size. We make the following key assumption: The spatiotemporal analysis in the second step of the divide-and-conquer strategy uses known, fixed spatial and temporal search radii, as determining split positions would be very difficult otherwise. Our results show that ST-FLEX-D is successful in reducing data replication across a range of parameterizations but comes at the expense of increased decomposition time. Our approach is portable to other space-time analysis methods and holds the potential to enable scalable geospatial applications.