Abstract
Given an n-point metric (P,d) and an integer k > 0, we consider the problem of covering P by k balls so as to minimize the sum of the radii of the balls. We present a randomized algorithm that runs in n O(logn ·logΔ) time and returns with high probability the optimal solution. Here, Δ is the ratio between the maximum and minimum interpoint distances in the metric space. We also show that the problem is NP-hard, even in metrics induced by weighted planar graphs and in metrics of constant doubling dimension.
Work by the first, second, third, and fifth authors was partially supported by NSF CAREER award CCR 0237431.
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Gibson, M., Kanade, G., Krohn, E., Pirwani, I.A., Varadarajan, K. (2008). On Metric Clustering to Minimize the Sum of Radii. In: Gudmundsson, J. (eds) Algorithm Theory – SWAT 2008. SWAT 2008. Lecture Notes in Computer Science, vol 5124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69903-3_26
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DOI: https://doi.org/10.1007/978-3-540-69903-3_26
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