Weighted Closest Pairs

Michael Formann Institut für Informatik Freie Universität Berlin Report B 92-04 February 92

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In this paper we study the following {\it weighted closest pair problem}: Given a set of planar objects with centerpoints, determine the {\it maximal scaling factor} $\delta_{max}$, such that the objects scaled by $\delta_{max}$ are pairwise disjoint. We describe a method to compute the maximal scaling factor in optimal $\bigO(n\log n)$ time for a wide class of objects, including disks generated by $L_p$-norms ($1 \leq p \leq \infty$).