Vietoris-Rips complexes of planar point sets

DOI10.1007/s00454-009-9209-8zbMath1231.05306arXiv0712.0395OpenAlexW1980200998MaRDI QIDQ977181

Jeff Erickson, Vin De Silva, Erin Wolf Chambers, Robert W. Ghrist

Publication date: 21 June 2010

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.0395

zbMATH Keywords

topologyRips complexquasi-Rips complex

Mathematics Subject Classification ID

Combinatorial aspects of simplicial complexes (05E45)

Related Items (18)

The Vietoris-Rips complexes of a circle ⋮ Geometric Approaches to Persistent Homology ⋮ Bestvina–Brady discrete Morse theory and Vietoris–Rips complexes ⋮ The Persistent Homology of Cyclic Graphs ⋮ On the Reconstruction of Geodesic Subspaces of ℝN ⋮ Footprints of geodesics in persistent homology ⋮ On Vietoris-Rips complexes of hypercube graphs ⋮ On homotopy types of Euclidean Rips complexes ⋮ Vietoris-Rips complexes of metric spaces near a metric graph ⋮ On Vietoris–Rips Complexes (with Scale 3) of Hypercube Graphs ⋮ Random geometric complexes ⋮ Geometry-driven collapses for converting a Čech complex into a triangulation of a nicely triangulable shape ⋮ Metric thickenings of Euclidean submanifolds ⋮ Mayer-Vietoris sequences and coverage problems in sensor networks ⋮ Complexity of simplicial homology and independence complexes of chordal graphs ⋮ Extremal Betti numbers of Vietoris-Rips complexes ⋮ Distributed computation of coverage in sensor networks by homological methods ⋮ Unnamed Item

Cites Work

• Unnamed Item
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• On the local behavior of spaces of natural images
• Coverage in sensor networks via persistent homology
• Finding the homology of submanifolds with high confidence from random samples
• Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology
• Testing contractibility in planar rips complexes
• Local approximation schemes for topology control
• PERSISTENCE BARCODES FOR SHAPES
• AN ALGEBRAIC TOPOLOGICAL METHOD FOR FEATURE IDENTIFICATION

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