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Minimum Dilation Stars

David Eppstein·Kevin A. Wortman
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Abstract

The dilation of a Euclidean graph is defined as the ratio of distance in the graph divided by distance in R^d. In this paper we consider the problem of positioning the root of a star such that the dilation of the resulting star is minimal. We present a deterministic O(n log n)-time algorithm for evaluating the dilation of a given star; a randomized O(n log n) expected-time algorithm for finding an optimal center in R^d; and for the case d=2, a randomized O(n 2^(alpha(n)) log^2 n) expected-time algorithm for finding an optimal center among the input points.

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BibTeXRIS

David Eppstein, Kevin A. Wortman. 2005-03-16. Minimum Dilation Stars. https://doi.org/10.1016/j.comgeo.2006.05.007

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