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Curve reconstruction, the Traveling Salesman Problem, and Menger’s theorem on length. (English) Zbl 0984.65012

The author gives necessary and sufficient regularity conditions under which the polygonal reconstruction of curves solved by a travelling salesman tour or path, extending a theorem of K. Menger [Math. Ann. 103, 467-501 (1932; JFM 56.0508.04)] on arc length for simple open curves to closed curves in Euclidean spaces.
Reviewer: M.Hager (Leonberg)

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
90C27 Combinatorial optimization
90C35 Programming involving graphs or networks

Citations:

JFM 56.0508.04
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