Xue, J and Li, Y and Rahul, S and Janardan, R (2022) New Bounds for Range Closest-Pair Problems. In: Discrete and Computational Geometry, 68 (1). pp. 1-49.
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Abstract
Given a dataset S of points in R2, the range closest-pair (RCP) problem aims to preprocess S into a data structure such that when a query range X is specified, the closest-pair in S∩ X can be reported efficiently. The RCP problem can be viewed as a range-search version of the classical closest-pair problem, and finds applications in many areas. Due to its non-decomposability, the RCP problem is much more challenging than many traditional range-search problems. This paper revisits the RCP problem, and proposes new data structures for various query types including quadrants, strips, rectangles, and halfplanes. Both worst-case and average-case analyses (in the sense that the data points are drawn uniformly and independently from the unit square) are applied to these new data structures, which result in new bounds for the RCP problem. Some of the new bounds significantly improve the previous results, while the others are entirely new.
| Item Type: | Journal Article |
|---|---|
| Publication: | Discrete and Computational Geometry |
| Publisher: | Springer |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Closest pair; Geometric data structures; Range search |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 21 Sep 2022 05:56 |
| Last Modified: | 21 Sep 2022 05:56 |
| URI: | https://eprints.iisc.ac.in/id/eprint/76610 |
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