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Minisum Location with Closest Euclidean Distances
Annals of Operations Research, 2002In previous papers, the authors of this paper formulated a single facility minisum location problem, where the set of customers as well as the new facility may be represented as areas on the plane and the rectangular norm was used as the distance function [see Naval Res. Logist. 47, 77--84 (2000; Zbl 0953.90033) and Comput. Oper. Res.
Jack Brimberg, George O. Wesolowsky
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Graph Distance and Euclidean Distance on the Grid
1990Given a connected graph G = (V, E),V = Z2, on the lattice points of the plane, let d G (p, q) and d(p,q) denote the graph distance and the Euclidean distance between p and q respectively. In this note we prove that for every є > 0 there is a graph G = Gє and a constant d = dє such that $$\left| {{d}_{G}}(p,q)-d(p,q) \right|
J. Pach, R. Pollack, J. Spencer
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The Mathematics Teacher, 1971
There are basically two approaches to classical Euclidean plane geometry—the synthetic approach and the metric approach. The older of the two is the synthetic approach followed by Eucliding later by Hilbert. In the Eucliding treatment, one begin by assuming as undefined the relations of betweenness, congruence of segments, and congruence of angles. The
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There are basically two approaches to classical Euclidean plane geometry—the synthetic approach and the metric approach. The older of the two is the synthetic approach followed by Eucliding later by Hilbert. In the Eucliding treatment, one begin by assuming as undefined the relations of betweenness, congruence of segments, and congruence of angles. The
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Mahalanobis and Euclidean Distances
NIR news, 2010Two distance measures Figures 1 and 2 each show the same twodimensional scatter plot of 20 points, plus one extra point in red. Each point corresponds to a spectrum, in this case measured at only two wavelengths, with one axis for the absorbance at each wavelength: not terribly realistic, but I cannot draw pictures in high dimensions.
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On Euclidean and Teichmüller Distances
2018Let (X1, q1) and (X2, q2) be Riemann surfaces with quadratic differentials whose associated,flat metrics have unit area and are -close with respect to a metric built from good systems,of period coordinates. Assume X1, X2 lie over a compact subset K of the moduli space of,Riemann surfaces Mg,n.
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Comparison of Euclidean Approximations of non-Euclidean Distances
1999The different techniques used for Euclidean approximation of distances are discussed. In the special case of points in a Euclidean space, whose distances are biased due to measure errors, accepting negative eigenvalues may help in the interpretation of results that are less biased than those obtained through an additive constant solution.
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Generalized Euclidean distance matrices
Linear and Multilinear Algebra, 2022R B Bapat, Shivani Goel
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2D Euclidean distance transform algorithms
ACM Computing Surveys, 2008Luciano da Fontoura Costa +1 more
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