Computing colourful simplicial depth and Median in \(\mathbb{R}_2\)

DOI10.1007/s00224-021-10067-4OpenAlexW4206007017MaRDI QIDQ2135626

Olga Zasenko, Tamon Stephen, Greg Aloupis

Publication date: 9 May 2022

Published in: Theory of Computing Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00224-021-10067-4

zbMATH Keywords

simplicial depthcolourful simplicial depthsimplicial median2d computational geometry

Mathematics Subject Classification ID

Mathematical programming (90Cxx) Graph theory (05Cxx) Computing methodologies and applications (68Uxx)

Uses Software

• AS 307
• GitHub

Cites Work

• Unnamed Item
• The colourful simplicial depth conjecture
• On Gromov's method of selecting heavily covered points
• On a triangle counting problem
• On a notion of data depth based on random simplices
• The colourful feasibility problem
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• Topologically sweeping an arrangement
• A generalization of Caratheodory's theorem
• Geometric medians
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• Lower bounds for computing statistical depth.
• Colorful linear programming, Nash equilibrium, and pivots
• Computational aspects of the colorful Carathéodory theorem
• Colourful simplicial depth
• Algorithms for Colourful Simplicial Depth and Medians in the Plane
• On Crossing Numbers of Complete Tripartite and Balanced Complete Multipartite Graphs
• Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
• Crossing-Free Subgraphs
• Colourful Linear Programming and its Relatives
• Algorithm AS 307: Bivariate Location Depth
• From Crossing-Free Graphs on Wheel Sets to Embracing Simplices and Polytopes with Few Vertices
• Colorful Simplicial Depth, Minkowski Sums, and Generalized Gale Transforms
• FINDING SIMPLICES CONTAINING THE ORIGIN IN TWO AND THREE DIMENSIONS