2017/12/28 by Jie Xue, Xue, Jie, Yuan Li +5 · 1 citation
Computer Science · Mathematics · #Algorithm #Algorithms and Data Compression #Combinatorics #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Computer science #Data Management and Algorithms #Data structure #Discrete mathematics #F.2.2 #FOS: Computer and information sciences #Geometry #Mathematics #Range (aeronautics) #Square (algebra) #Unit square #cs.CG
paper · pdf · doi:10.48550/arxiv.1712.09749
published in ArXiv.org
openalex publication_date 2017/12/28 · arxiv created 2018/03/31 · arxiv updated 2018/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.