Efficient Constrained Delaunay Triangulation for Large Spatial Databases

Delaunay Triangulation (DT) and its extension Constrained Delaunay Triangulation (CDT) are spatial data structures that have wide applications in spatial data processing. Our recent survey shows, however, that there is a surprising lack of algorithms for computing DT/CDT for large spatial databases. In view of this, we propose an efficient algorithm based on the divide and conquer paradigm. It computes DT/CDT on in-memory partitions before merging them into the final result. This is made possible by discovering mathematical property that precisely characterizes the set of triangles that are involved in the merging step. Our extensive experiments show that the new algorithm outperforms another provably good disk-based algorithm by roughly an order of magnitude when computing DT. For CDT, which has no known disk-based algorithm, we show that our algorithm scales up well for large databases with size in the range of gigabytes.