Adaptive parallel Delaunay triangulation construction with dynamic pruned binary tree model in Cloud

The paper illustrates a parallel and distributed scheme for computing a planar Delaunay triangulation using a divide-and-conquer strategy in Cloud environment, which combines the incremental insertion algorithm and the divide-and-conquer method. The proposed hybrid algorithm for Delaunay triangulation construction is easy to be parallelized due to the dynamic pruned characteristic of the binary tree model used. Moreover, the Cloud platform decreases the communication overhead and improves data locality by making use of a data partitioning and integrating scheme offered by the map-reduce architecture. The implementation of the parallel and distributed version of the algorithm relied on a robust data structure called quad-edge, which implies the geometric relationship among the edges and vertexes adjacent. More importantly, the data are serialized easily and transmitted efficiently between different Cloud nodes; the algorithm is executed conveniently on PC clusters. We tested the parallel version of the algorithm on GeoKSCloud, a geographical knowledge service Cloud developed by our research team. Experimental results show that the proposed hybrid algorithm is efficient and competitive; it can be easily migrated and deployed in distributed and parallel computing environment, such as grid and Cloud. The parallel implementation of the hybrid algorithm has a good speed-up, while data communication is the crucial factor for the efficiency of the parallel version. Overall, the parallel version outperforms both the sequential divide-and-conquer algorithm and the sequential incremental insertion algorithm.