TY - GEN
T1 - New bounds for range closest-pair problems
AU - Xue, Jie
AU - Li, Yuan
AU - Rahul, Saladi
AU - Janardan, Ravi
N1 - Publisher Copyright:
© Jie Xue, Yuan Li, Saladi Rahul, and Ravi Janardan; licensed under Creative Commons License CC-BY 34th Symposium on Computational Geometry (SoCG 2018).
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - 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.
AB - 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.
KW - Average-case analysis
KW - Candidate pairs
KW - Closest-pair
KW - Range search
UR - http://www.scopus.com/inward/record.url?scp=85048974993&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85048974993&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.SoCG.2018.73
DO - 10.4230/LIPIcs.SoCG.2018.73
M3 - Conference contribution
AN - SCOPUS:85048974993
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 731
EP - 7314
BT - 34th International Symposium on Computational Geometry, SoCG 2018
A2 - Toth, Csaba D.
A2 - Speckmann, Bettina
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 34th International Symposium on Computational Geometry, SoCG 2018
Y2 - 11 June 2018 through 14 June 2018
ER -