OpenACC Based GPU Parallelization of Plane Sweep Algorithm for Geometric Intersection

Line segment intersection is one of the elementary operations in computational geometry. Complex problems in Geographic Information Systems (GIS) like finding map overlays or spatial joins using polygonal data require solving segment intersections. Plane sweep paradigm is used for finding geometric intersection in an efficient manner. However, it is difficult to parallelize due to its in-order processing of spatial events. We present a new fine-grained parallel algorithm for geometric intersection and its CPU and GPU implementation using OpenMP and OpenACC. To the best of our knowledge, this is the first work demonstrating an effective parallelization of plane sweep on GPUs. We chose compiler directive based approach for implementation because of its simplicity to parallelize sequential code. Using Nvidia Tesla P100 GPU, our implementation achieves around 40X speedup for line segment intersection problem on 40K and 80K data sets compared to sequential CGAL library

Hierarchical and Adaptive Filter and Refinement Algorithms for Geometric Intersection Computations on GPU

Geometric intersection algorithms are fundamental in spatial analysis in Geographic Information System (GIS). This dissertation explores high performance computing solution for geometric intersection on a huge amount of spatial data using Graphics Processing Unit (GPU). We have developed a hierarchical filter and refinement system for parallel geometric intersection operations involving large polygons and polylines by extending the classical filter and refine algorithm using efficient filters that leverage GPU computing. The inputs are two layers of large polygonal datasets and the computations are spatial intersection on pairs of cross-layer polygons. These intersections are the compute-intensive spatial data analytic kernels in spatial join and map overlay operations in spatial databases and GIS. Efficient filters, such as PolySketch, PolySketch++ and Point-in-polygon filters have been developed to reduce refinement workload on GPUs. We also showed the application of such filters in speeding-up line segment intersections and point-in-polygon tests. Programming models like CUDA and OpenACC have been used to implement the different versions of the Hierarchical Filter and Refine (HiFiRe) system. Experimental results show good performance of our filter and refinement algorithms. Compared to standard R-tree filter, on average, our filter technique can still discard 76% of polygon pairs which do not have segment intersection points. PolySketch filter reduces on average 99.77% of the workload of finding line segment intersections. Compared to existing Common Minimum Bounding Rectangle (CMBR) filter that is applied on each cross-layer candidate pair, the workload after using PolySketch-based CMBR filter is on average 98% smaller. The execution time of our HiFiRe system on two shapefiles, namely USA Water Bodies (contains 464K polygons) and USA Block Group Boundaries (contains 220K polygons), is about 3.38 seconds using NVidia Titan V GPU

Hierarchical Filter and Refinement System Over Large Polygonal Datasets on CPU-GPU

In this paper, we introduce our hierarchical filter and refinement technique that we have developed for parallel geometric intersection operations involving large polygons and polylines. The inputs are two layers of large polygonal datasets and the computations are spatial intersection on a pair of cross-layer polygons. These intersections are the compute-intensive spatial data analytic kernels in spatial join and map overlay computations. We have extended the classical filter and refine algorithms using PolySketch Filter to improve the performance of geospatial computations. In addition to filtering polygons by their Minimum Bounding Rectangle (MBR), our hierarchical approach explores further filtering using tiles (smaller MBRs) to increase the effectiveness of filtering and decrease the computational workload in the refinement phase. We have implemented this filter and refine system on CPU and GPU by using OpenMP and OpenACC. After using R-tree, on average, our filter technique can still discard 69% of polygon pairs which do not have segment intersection points. PolySketch filter reduces on average 99.77% of the workload of finding line segment intersections. PNP based task reduction and Striping algorithms filter out on average 95.84% of the workload of Point-in-Polygon tests. Our CPU-GPU system performs spatial join on two shapefiles, namely USA Water Bodies and USA Block Group Boundaries with 683K polygons in about 10 seconds using NVidia Titan V and Titan Xp GPU

AZB Rectangle Shrinkage Method and Heterogeneous Computing Accelerated Full Image Theory Method Ray Tracing Enabling Complex and Massive Outdoor 6G Propagation Modeling

Until now, despite their high accuracy, the utilization of the conventional image theory method ray tracers was limited to simple simulation environments with small number of field observation points and low maximum ray bouncing order due to their poor computational efficiency. This study presents a novel full-3D AZB rectangle shrinkage method and heterogeneous computing accelerated image theory method ray tracing framework for complex and massive outdoor propagation modeling. The proposed framework is divided into three parts: 1. Visibility preprocessing part. 2. Visibility tree generation part: in this part, a novel AZB rectangle shrinkage method that accelerates and reduces generation speed and size of visibility tree is proposed. 3. Shadow testing and field calculation part: in this part, a heterogeneous computing algorithm that can make possible to handle a large amount of field observation points is proposed. It is demonstrated that the proposed framework is faster more than 651 times than the image theory method solver of WinProp. Also, it is confirmed that the proposed ray tracing framework can handle 1km x 1km wide and dense urban outdoor simulation with up to the maximum ray bouncing order of 6 and thousands of field observation points. The proposed ray tracing framework would be a cornerstone of future image theory method ray tracing techniques for complex and massive scenarios that was exclusive to the shooting and bouncing rays method ray tracers

A Heterogeneous High Performance Computing Framework For Ill-Structured Spatial Join Processing

The frequently employed spatial join processing over two large layers of polygonal datasets to detect cross-layer polygon pairs (CPP) satisfying a join-predicate faces challenges common to ill-structured sparse problems, namely, that of identifying the few intersecting cross-layer edges out of the quadratic universe. The algorithmic engineering challenge is compounded by GPGPU SIMT architecture. Spatial join involves lightweight filter phase typically using overlap test over minimum bounding rectangles (MBRs) to discard majority of CPPs, followed by refinement phase to rigorously test the join predicate over the edges of the surviving CPPs. In this dissertation, we develop new techniques - algorithms, data structure, i/o, load balancing and system implementation - to accelerate the two-phase spatial-join processing. We present a new filtering technique, called Common MBR Filter (CMF), which changes the overall characteristic of the spatial join algorithms wherein the refinement phase is no longer the computational bottleneck. CMF is designed based on the insight that intersecting cross-layer edges must lie within the rectangular intersection of the MBRs of CPPs, their common MBRs (CMBR). We also address a key limitation of CMF for class of spatial datasets with either large or dense active CMBRs by extended CMF, called CMF-grid, that effectively employs both CMBR and grid techniques by embedding a uniform grid over CMBR of each CPP, but of suitably engineered sizes for different CPPs. To show efficiency of CMF-based filters, extensive mathematical and experimental analysis is provided. Then, two GPU-based spatial join systems are proposed based on two CMF versions including four components: 1) sort-based MBR filter, 2) CMF/CMF-grid, 3) point-in-polygon test, and, 4) edge-intersection test. The systems show two orders of magnitude speedup over the optimized sequential GEOS C++ library. Furthermore, we present a distributed system of heterogeneous compute nodes to exploit GPU-CPU computing in order to scale up the computation. A load balancing model based on Integer Linear Programming (ILP) is formulated for this system. We also provide three heuristic algorithms to approximate the ILP. Finally, we develop MPI-cuda-GIS system based on this heterogeneous computing model by integrating our CUDA-based GPU system into a newly designed distributed framework designed based on Message Passing Interface (MPI). Experimental results show good scalability and performance of MPI-cuda-GIS system

Load Balancing Algorithms for Parallel Spatial Join on HPC Platforms

Geospatial datasets are growing in volume, complexity, and heterogeneity. For efficient execution of geospatial computations and analytics on large scale datasets, parallel processing is necessary. To exploit fine-grained parallel processing on large scale compute clusters, partitioning of skewed datasets in a load-balanced way is challenging. The workload in spatial join is data dependent and highly irregular. Moreover, wide variation in the size and density of geometries from one region of the map to another, further exacerbates the load imbalance. This dissertation focuses on spatial join operation used in Geographic Information Systems (GIS) and spatial databases, where the inputs are two layers of geospatial data, and the output is a combination of the two layers according to join predicate.This dissertation introduces a novel spatial data partitioning algorithm geared towards load balancing the parallel spatial join processing. Unlike existing partitioning techniques, the proposed partitioning algorithm divides the spatial join workload instead of partitioning the individual datasets separately to provide better load-balancing. This workload partitioning algorithm has been evaluated on a high-performance computing system using real-world datasets. An intermediate output-sensitive duplication avoidance technique is proposed that decreases the external memory space requirement for storing spatial join candidates across the partitions. GPU acceleration is used to further reduce the spatial partitioning runtime. For dynamic load balancing in spatial join, a novel framework for fine-grained work stealing is presented. This framework is efficient and NUMA-aware. Performance improvements are demonstrated on shared and distributed memory architectures using threads and message passing. Experimental results show effective mitigation of data skew. The framework supports a variety of spatial join predicates and spatial overlay using partitioned and un-partitioned datasets

The use of primitives in the calculation of radiative view factors

Compilations of radiative view factors (often in closed analytical form) are readily available in the open literature for commonly encountered geometries. For more complex three-dimensional (3D) scenarios, however, the effort required to solve the requisite multi-dimensional integrations needed to estimate a required view factor can be daunting to say the least. In such cases, a combination of finite element methods (where the geometry in question is sub-divided into a large number of uniform, often triangular, elements) and Monte Carlo Ray Tracing (MC-RT) has been developed, although frequently the software implementation is suitable only for a limited set of geometrical scenarios. Driven initially by a need to calculate the radiative heat transfer occurring within an operational fibre-drawing furnace, this research set out to examine options whereby MC-RT could be used to cost-effectively calculate any generic 3D radiative view factor using current vectorisation technologies

Gunrock: GPU Graph Analytics

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs, have presented two significant challenges to developing a programmable high-performance graph library. "Gunrock", our graph-processing system designed specifically for the GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high performance GPU computing primitives and optimization strategies with a high-level programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. We characterize the performance of various optimization strategies and evaluate Gunrock's overall performance on different GPU architectures on a wide range of graph primitives that span from traversal-based algorithms and ranking algorithms, to triangle counting and bipartite-graph-based algorithms. The results show that on a single GPU, Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives and CPU shared-memory graph libraries such as Ligra and Galois, and better performance than any other GPU high-level graph library.Comment: 52 pages, invited paper to ACM Transactions on Parallel Computing (TOPC), an extended version of PPoPP'16 paper "Gunrock: A High-Performance Graph Processing Library on the GPU