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 α ( n ) log 2 n ) expected-time algorithm for finding an optimal center among the input points.

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