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arXiv · 1310.3388

Finding the Largest Disk Containing a Query Point in Logarithmic Time with Linear Storage

Tal Kaminker·Micha Sharir
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Abstract

Let D be a set of n disks in the plane. We present a data structure of size O(n) that can compute, for any query point q, the largest disk in D that contains q, in O(log n) time. The structure can be constructed in O(n log^3 n) time. The optimal storage and query time of the structure improve several recent solutions by Augustine et al. and by Kaplan and Sharir.

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Tal Kaminker, Micha Sharir. 2013-10-12. Finding the Largest Disk Containing a Query Point in Logarithmic Time with Linear Storage. https://arxiv.org/abs/1310.3388

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