Flow computations on imprecise terrains

Abstract

We study the computation of the flow of water on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water can only flow along the edges of a predefined graph (for example a grid, a triangulation, or its dual), possibly non-planar, and one where water flows across the surface of a polyhedral terrain in the direction of steepest descent. In both cases each vertex has an imprecise height, given by an interval of possible values, while its (x,y)-coordinates are fixed. For the first model, we give a simple O(n log n) time algorithm to compute the maximal watershed of a vertex, where n is the number of edges of the graph. We show that, in contrast, in the second model the problem of deciding whether one vertex may be contained in the watershed of another is NP-hard