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New Bounds for Range Closest-Pair Problems

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



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Jie Xue
Yuan Li
Saladi Rahul
Ravi Janardan

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Jie Xue, Yuan Li, Saladi Rahul, and Ravi Janardan. New Bounds for Range Closest-Pair Problems. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 73:1-73:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.SoCG.2018.73

Abstract

Given a dataset S of points in R^2, 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 cap 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.
Keywords
  • Closest-pair
  • Range search
  • Candidate pairs
  • Average-case analysis

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