Abstract
In this paper we study the following scaling problem: Given a set of planar starshaped objects with centerpoints (in the kernel), determine the maximal scaling factor δ max, such that the objects scaled by δ max about their centerpoints are pairwise disjoint.
We describe a method to compute the maximal scaling factor for n disks with different radii in optimal O(n log n) time. In this case the problem can be viewed as computing the closest pair of a set of weighted points.
We indicate how to extend the method to a broader class of objects, including disks generated by L p -norms (1 ≤ p ≤ ∞).
A different approach, using the parametric search technique is taken to solve the scaling problem for an even wider class, namely starshaped, x-monotone objects. This method runs in O(n log2 n) time. As a corollary of this result we can compute the maximal scaling factor of a set of starshaped polygons (not necessarily x-monotone) with a total number of n edges in O(n log2 n) time.
This work was partially supported by the ESPRIT Basic Research Action of the European Community under contract No. 7141 (project ALCOM II).
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© 1993 Springer-Verlag Berlin Heidelberg
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Formann, M. (1993). Weighted closest pairs. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_28
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DOI: https://doi.org/10.1007/3-540-56503-5_28
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