Curve reconstruction, the traveling salesman problem and Menger's theorem on length
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Summary
It is given necessary and sufficient regularity conditions under which the curve reconstruction problem is solved by a traveling salesman tour or path, respectively.
- Type
- article
- Published
- 1999-06-13
- Cited by
- 45
- References
- 20
- Access
- Open access
- OpenAlex
- https://openalex.org/W2022116306
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:244673
Keywords
Travelling salesman problem, Citation, Combinatorics, Computer science, Mathematics
References
- Real Analysis: Modern Techniques and Their Applications
- Ergebnisse eines Mathematischen Kolloquiums
- Crust and anti-crust: a one-step boundary and skeleton extraction algorithm
- The Crust and the beta-Skeleton: Combinatorial Curve Reconstruction
- Curve reconstruction: connecting dots with good reason
- Integral curvature of a curve in n-dimensional Euclidean space
- A simple provable algorithm for curve reconstruction
- Some applications of integral geometry to the theory of curves of finite rotation
- Sampling and reconstructing manifolds using alpha-shapes
- The geometry of fractal sets: Contents
- Experiments on Curve Reconstruction
- TSP-based curve reconstruction in polynomial time
- Curve Reconstruction in Arbitrary Dimension and the Traveling Salesman Problem
- Untersuchungen über allgemeine Metrik. Vierte Untersuchung. Zur Metrik der Kurven
Cited by
- Fat Triangulations and Differential Geometry
- Analysis of Curve Reconstruction by Meshless Parameterization
- Reconstructing a collection of curves with corners and endpoints
- Geometric approach to sampling and communication
- EXPERIMENTAL APPROACH TO CURVE RECONSTRUCTION BASED ON HUMAN VISUAL PERCEPTION
- Pseudo-temporal ordering of individual cells reveals dynamics and regulators of cell fate decisions
- Unsupervised Discovery of Subspace Trends
- A distance-based parameter free algorithm for curve reconstruction
- Approximative graph pyramid solution of the E-TSP
- Curve reconstruction: connecting dots with good reason
- Surface reconstruction using umbrella filters
- Reconstruction curves with sharp corners
- Smooth surface reconstruction via natural neighbour interpolation of distance functions
- A simple algorithm for homeomorphic surface reconstruction
- The power crust, unions of balls, and the medial axis transform
- Reconstructing Curves without Delaunay Computation
- Fast Reconstruction of Curves with Sharp Corners
- Reconstructing the Temporal Ordering of Biological Samples Using Microarray Data
- Combinatorial curve reconstruction in Hilbert spaces: A new sampling theory and an old result revisited
- VICUR: A human-vision-based algorithm for curve reconstruction
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