I/O-Efficient Map Overlay and Point Location in Low-Density Subdivisions [chapter]

Mark de Berg, Herman Haverkort, Shripad Thite, Laura Toma
2007 Lecture Notes in Computer Science  
We present improved and simplified i/o-efficient algorithms for two problems on planar low-density subdivisions, namely map overlay and point location. More precisely, we show how to preprocess a lowdensity subdivision with n edges in O(sort (n)) i/o's into a compressed linear quadtree such that one can: (i) compute the overlay of two preprocessed subdivisions in O(scan (n)) i/o's, where n is the total number of edges in the two subdivisions, (ii) answer a single point location query in O(log B
more » ... n) i/o's and k batched point location queries in O(scan (n) + sort (k)) i/o's. For the special case where the subdivision is a fat triangulation, we show how to obtain the same bounds with an ordinary (uncompressed) quadtree, and we show how to make the structure fully dynamic using O(log B n) i/o's per update. Our algorithms and data structures improve on the previous best known bounds for general subdivisions both in the number of i/o's and storage usage, they are significantly simpler, and several of our algorithms are cache-oblivious.
doi:10.1007/978-3-540-77120-3_44 fatcat:kuwc7ktx3vcnzmoxjtcgxpxniu