Computational geometry: an introduction
Computational geometry: an introduction
Visualization of scalar topology for structural enhancement
Proceedings of the conference on Visualization '98
GRIN'01 No description on Graphics interface 2001
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
A Multi-resolution Data Structure for Two-dimensional Morse-Smale Functions
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Weighted isotonic regression under the L1 norm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Persistence-sensitive simplification functions on 2-manifolds
Proceedings of the twenty-second annual symposium on Computational geometry
I/O-efficient batched union-find and its applications to terrain analysis
Proceedings of the twenty-second annual symposium on Computational geometry
TerraStream: from elevation data to watershed hierarchies
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Unimodal regression via prefix isotonic regression
Computational Statistics & Data Analysis
Algorithms and theory of computation handbook
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We describe algorithms for finding the regression of t, a sequence of values, to the closest sequence s by mean squared error, so that s is always increasing (isotonicity) and so the values of two consecutive points do not increase by too much (Lipschitz). The isotonicity constraint can be replaced with a unimodular constraint, for exactly one local maximum in s. These algorithm are generalized from sequences of values to trees of values. For each we describe near-linear time algorithms.