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arXiv · cs/0602029

Approximate Weighted Farthest Neighbors and Minimum Dilation Stars

John Augustine·David Eppstein·Kevin A. Wortman
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Abstract

We provide an efficient reduction from the problem of querying approximate multiplicatively weighted farthest neighbors in a metric space to the unweighted problem. Combining our techniques with core-sets for approximate unweighted farthest neighbors, we show how to find (1+epsilon)-approximate farthest neighbors in time O(log n) per query in D-dimensional Euclidean space for any constants D and epsilon. As an application, we find an O(n log n) expected time algorithm for choosing the center of a star topology network connecting a given set of points, so as to approximately minimize the maximum dilation between any pair of points.

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John Augustine, David Eppstein, Kevin A. Wortman. 2006-02-07. Approximate Weighted Farthest Neighbors and Minimum Dilation Stars. https://arxiv.org/abs/cs/0602029

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