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Searching for the Closest-pair in a Query Translate by Xue, Jie; Li, Yuan; Rahul, Saladi; Janardan, Ravi is a scholarly article available to read on EtoBox.

What is Searching for the Closest-pair in a Query Translate about?

We consider a range-search variant of the closest-pair problem. Let $\varGamma$ be a fixed shape in the plane. We are interested in storing a given set of $n$ points in the plane in some data structure such that for any specified translate of $\varGamma$, the closest pair of points contained in the translate can be reported efficiently. We present results on this problem for two important settings: when $\varGamma$ is a polygon (possibly with holes) and when $\varGamma$ is a general convex body whose boundary is smooth. When $\varGamma$ is a polygon, we present a data structure using $O(n)$ space and $O(\log n)$ query time, which is asymptotically optimal. When $\varGamma$ is a general convex body with a smooth boundary, we give a near-optimal data structure using $O(n \log n)$ space and $O(\log^2 n)$ query time. Our results settle some open questions posed by Xue et al. [SoCG 2018].

Author

Xue, Jie; Li, Yuan; Rahul, Saladi; Janardan, Ravi

Published

2018

Language

EN