Date of Award
Doctor of Philosophy (PhD)
Polygon clipping is one of the complex operations in computational geometry. It is used in Geographic Information Systems (GIS), Computer Graphics, and VLSI CAD. For two polygons with n and m vertices, the number of intersections can be O(nm). In this dissertation, we present the first output-sensitive CREW PRAM algorithm, which can perform polygon clipping in O(log n) time using O(n + k + k') processors, where n is the number of vertices, k is the number of intersections, and k' is the additional temporary vertices introduced due to the partitioning of polygons. The current best algorithm by Karinthi, Srinivas, and Almasi does not handle self-intersecting polygons, is not output-sensitive and must employ O(n^2) processors to achieve O(log n) time. The second parallel algorithm is an output-sensitive PRAM algorithm based on Greiner-Hormann algorithm with O(log n) time complexity using O(n + k) processors. This is cost-optimal when compared to the time complexity of the best-known sequential plane-sweep based algorithm for polygon clipping. For self-intersecting polygons, the time complexity is O(((n + k) log n log log n)/p) using p
In addition to these parallel algorithms, the other main contributions in this dissertation are 1) multi-core and many-core implementation for clipping a pair of polygons and 2) MPI-GIS and Hadoop Topology Suite for distributed polygon overlay using a cluster of nodes. Nvidia GPU and CUDA are used for the many-core implementation. The MPI based system achieves 44X speedup while processing about 600K polygons in two real-world GIS shapefiles 1) USA Detailed Water Bodies and 2) USA Block Group Boundaries) within 20 seconds on a 32-node (8 cores each) IBM iDataPlex cluster interconnected by InfiniBand technology.
Puri, Satish, "Efficient Parallel and Distributed Algorithms for GIS Polygon Overlay Processing." Dissertation, Georgia State University, 2015.