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 approximate farthest neighbors that are farther than a factor (1 − ε) of optimal in time O(logn) per query in D-dimensional Euclidean space for any constants D and ε. As an application, we find an O(n logn) 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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Augustine, J., Eppstein, D., Wortman, K.A. (2010). Approximate Weighted Farthest Neighbors and Minimum Dilation Stars. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_12
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DOI: https://doi.org/10.1007/978-3-642-14031-0_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14030-3
Online ISBN: 978-3-642-14031-0
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