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.
Original language | English (US) |
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Pages (from-to) | 1-49 |
Number of pages | 49 |
Journal | Discrete and Computational Geometry |
Volume | 68 |
Issue number | 1 |
DOIs | |
State | Published - Jul 2022 |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Closest pair
- Geometric data structures
- Range search