Minimum dilation stars

Authors:
David Eppstein;Kevin A. Wortman
Affiliations:
Department of Computer Science, Donald Bren School of Information & Computer Sciences, University of California, Irvine, USA;Department of Computer Science, Donald Bren School of Information & Computer Sciences, University of California, Irvine, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2007

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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(nlogn)-time algorithm for evaluating the dilation of a given star; a randomized O(nlogn) expected-time algorithm for finding an optimal center in R^d; and for the case d=2, a randomized O(n2^@a^(^n^)log^2n) expected-time algorithm for finding an optimal center among the input points.