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In this paper we consider imprecise terrains, that is, triangulated terrainswith a vertical error interval in the vertices. In particular, we study theproblem of removing as many local extrema (minima and maxima) as possible fromthe terrain. We show that removing only minima or only maxima can be doneoptimally in O(n log n) time, for a terrain with n vertices. Interestingly,however, removing both the minima and maxima simultaneously is NP-hard, and iseven hard to approximate within a factor of O(log log n) unless P=NP. Moreover,we show that even a simplified version of the problem where vertices can haveonly two different heights is already NP-hard, a result we obtain by provinghardness of a special case of 2-Disjoint Connected Subgraphs, a problem thathas lately received considerable attention from the graph-algorithms community.

Removing Local Extrema from Imprecise Terrains