Marshall Bern, David Eppstein, Leonidas Guibas, John Hershberger, Subhash Suri, Jan Wolter  Home/Search
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Abstract: . Let S be a set of points in IR d , each with a weight that is not known precisely, only known to fall within some range. What is the locus of the centroid of S? We prove that this locus is a convex polytope, the projection of a zonotope in IR d+1 . We derive complexity bounds and algorithms for the construction of these "centroid polytopes". 1 Introduction Suppose that S = fs 1 ; s 2 ; : : : ; s n g is a set of points in IR d and that each point s i has an unknown nonnegative... (Update)
Context of citations to this paper: More
...[9, 11, 21] and cyclic sta#ng [16] but the averages used in these problems do not typically involve weights. More recently, Bern et al. [2] have investigated problems of finding the possible weighted averages of a point set in which the weight of each point may vary in a...
.... a special case of a centroid polytope, the locus of possible weighted averages of points each with an unknown weight within a certain range [2]. For reduced convex hulls, each weight i has the same range [0; and the sum of the weights is constrained to be 1. In [2] we...
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BibTeX entry: (Update)
M. Bern, D. Eppstein, L. Guibas, J. Hershberger, S. Suri, and J. Wolter. The centroid of points with approximate weights. Manuscript, 1995. http://citeseer.ist.psu.edu/bern95centroid.html More
@inproceedings{ bern95centroid,
author = "Marshall W. Bern and David Eppstein and Leonidas J. Guibas and John Hershberger and Subhash Suri and Jan Wolter",
title = "The Centroid of Points with Approximate Weights",
booktitle = "European Symposium on Algorithms",
pages = "460-472",
year = "1995",
url = "citeseer.ist.psu.edu/bern95centroid.html" }
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