### Flow computations on imprecise terrains

#### Abstract

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, or a set of vertices, where n is the number of edges of the graph. On a grid model, we can compute the same in*O*(*n*) time.#### Full Text:

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