Algorithms for bivariate medians and a Fermat-Torricelli problem for lines.

DOI10.1016/S0925-7721(02)00173-6zbMath1039.62045OpenAlexW2031858761MaRDI QIDQ1395576

Greg Aloupis, Michael Soss, Stefan Langerman, Godfried T. Toussaint

Publication date: 1 July 2003

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0925-7721(02)00173-6

zbMATH Keywords

AlgorithmsComputational geometryFermat-Torricelli problemSimplicial depthOja depthEstimators of locationGeometric medians

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Estimation in multivariate analysis (62H12) Characterization and structure theory for multivariate probability distributions; copulas (62H05)

Related Items

Computing colourful simplicial depth and Median in \(\mathbb{R}_2\), Multivariate median filters and partial differential equations, On Liu's simplicial depth and Randles' interdirections, Algorithms for Colourful Simplicial Depth and Medians in the Plane, Penalty-based aggregation of multidimensional data, A proof of the Oja depth conjecture in the plane, On Combinatorial Depth Measures, Algorithms for bivariate zonoid depth, Oja centers and centers of gravity, Topological sweep of the complete graph, The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg, A lower bound for computing Oja depth, Optimal Algorithms for Geometric Centers and Depth

Uses Software

• AS 307
• AS 277

Cites Work

• The finite-sample breakdown point of the Oja bivariate median and of the corresponding half-samples version
• On a triangle counting problem
• On a notion of data depth based on random simplices
• Descriptive statistics for multivariate distributions
• The power of geometric duality revisited
• Topologically sweeping an arrangement
• Geometric medians
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• Lower bounds for computing statistical depth.
• On Generalizations of Conics and on a Generalization of the Fermat- Torricelli Problem
• Algorithm AS 307: Bivariate Location Depth
• A note on the Fermat-Torricelli point of a \(d\)-simplex
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