The input/output complexity of sorting and related problems
Communications of the ACM
Visibility problems for polyhedral terrains
Journal of Symbolic Computation
Introduction to Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Computing visibility on terrains in external memory
Journal of Experimental Algorithmics (JEA)
Viewsheds on terrains in external memory
SIGSPATIAL Special
Low-Complexity Intervisibility in Height Fields
Computer Graphics Forum
More efficient terrain viewshed computation on massive datasets using external memory
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
On IO-efficient viewshed algorithms and their accuracy
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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This paper describes the design and engineering of algorithms for computing visibility maps on massive grid terrains. Given a terrain T, specified by the elevations of points in a regular grid, and given a viewpoint v, the visibility map or viewshed of v is the set of grid points of T that are visible from v. We describe three new algorithms to compute the viewshed for any given terrain T and viewpoint v. The first two algorithms "sweep" the terrain by rotating a ray around the viewpoint while maintaining the terrain profile along the ray. On a terrain of n grid points, these algorithms run in O(n log n) time and O(sort(n)) I/Os in the I/O-model of Aggarwal and Vitter. The difference between the two algorithms is in the preprocessing before the sweep: the first algorithm sorts the grid points into concentric bands around the viewpoint; the second algorithm sorts the grid points into sectors around the viewpoint. The third algorithm sweeps the terrain centrifugally, growing a star-shaped region around the viewpoint while maintaining the approximate visible horizon of the terrain within the swept region. This algorithm runs in O(n) time and O(scan(n)) I/Os and is cache-oblivious. We tested our algorithms on NASA SRTM data, and found that our fastest new algorithm computes the viewshed of a terrain of 7.6 billion points (28.4 GiB) in 203 minutes on a machine with 0.5 GiB RAM and a laptop-speed hard drive. Depending on the data set, the new algorithm is 20 to 50 times faster than the algorithm from our previous work.