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This document discusses algorithms for point location and map overlay in low-density subdivisions. It introduces the problems of point location, where given a point in a map you find the containing region, and map overlay, where you compute intersections between edges of two maps. It describes challenges with massive geographic data and the need for external memory algorithms. The document presents algorithms for these problems on low-density triangulations and maps based on building compressed quadtrees indexed by a Z-order curve in external memory, allowing efficient point location, map overlay, and updates.


















































