Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
TerraStream: from elevation data to watershed hierarchies
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
The complexity of flow on fat terrains and its i/o-efficient computation
Computational Geometry: Theory and Applications
Implicit flow routing on terrains with applications to surface networks and drainage structures
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Removing local extrema from imprecise terrains
Computational Geometry: Theory and Applications
Flow on noisy terrains: an experimental evaluation
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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We study water flow computation on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water flows across the surface of a polyhedral terrain in the direction of steepest descent, and one where water only flows along the edges of a predefined graph, for example a grid or a triangulation. In both cases each vertex has an imprecise elevation, given by an interval of possible values, while its (x, y)-coordinates are fixed. For the first model, we show that the problem of deciding whether one vertex may be contained in the watershed of another is NP-hard. In contrast, for the second model we give a simple O(n log n) time algorithm to compute the minimal and the maximal watershed of a vertex, where n is the number of edges of the graph. On a grid model, we can compute the same in O(n) time.