A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
An outlet breaching algorithm for the treatment of closed depressions in a raster DEM
Computers & Geosciences
Proceedings of the 8th ACM international symposium on Advances in geographic information systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Higher order Delaunay triangulations
Computational Geometry: Theory and Applications
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Generating realistic terrains with higher-order Delaunay triangulations
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
An efficient depression processing algorithm for hydrologic analysis
Computers & Geosciences
An efficient depression processing algorithm for hydrologic analysis
Computers & Geosciences
Algorithm for dealing with depressions in dynamic landscape evolution models
Computers & Geosciences
Smoothing Imprecise 1.5D Terrains
Approximation and Online Algorithms
Embedding rivers in polyhedral terrains
Proceedings of the twenty-fifth annual symposium on Computational geometry
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In many applications of terrain analysis, pits or local minima are considered artifacts that must be removed before the terrain can be used. Most of the existing methods for local minima removal work only for raster terrains. In this paper we consider algorithms to remove local minima from polyhedral terrains, by modifying the heights of the vertices. To limit the changes introduced to the terrain, we try to minimize the total displacement of the vertices. Two approaches to remove local minima are analyzed: lifting vertices and lowering vertices. For the former we show that all local minima in a terrain with n vertices can be removed in the optimal way in O(n log n) time. For the latter we prove that the problem is NP-hard, and present an approximation algorithm with factor 2 ln k, where k is the number of local minima in the terrain.