A Parallel Algorithm for Computing Polygon Set Operations |
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Affiliation: | 1. University of Crete, Greece & ICS-FORTH, Greece;2. University of Athens, Greece;3. Athena Research Center, Greece;4. University of Tampere, Finland;5. Paris Descartes University, France;1. State Key Laboratory of Integrated Information System Technology, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China;2. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China;3. The University of Chinese Academy of Sciences, Beijing 100049, China |
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Abstract: | We present a parallel algorithm for performing boolean set operations on generalized polygons that have holes in them. The intersection algorithm has a processor complexity of O(m2n2) processors and a time complexity of O(max(2log m, log2n)), where m is the maximum number of vertices in any loop of a polygon, and n is the maximum number of loops per polygon. The union and difference algorithms have a processor complexity of O(m2n2) and time complexity of O(log m) and O(2log m, log n) respectively. The algorithm is based on the EREW PRAM model. The algorithm tries to minimize the intersection point computations by intersecting only a subset of loops of the polygons, taking advantage of the topological structure of the two polygons. We believe this will result in better performance on the average as compared to the worst case. Though all the algorithms presented here are deterministic, randomized algorithms such as sample sort can be used for the sorting subcomponent of the algorithms to obtain fast practical implementations. |
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