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Abstract: In this paper we study dynamic variants of conjugation trees and related structures that have recently been introduced for performing various types of queries on sets of points and line segments, like half-planar range searching, shooting, intersection queries, etc. For most of these types of queries dynamic structures are obtained with an amortized update time of O(log 2 n) (or less) with only minor increases in the query times. As an application of the method we obtain an... (Update)
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...a set of points in R d , and given a query half space, report all the points that lie in the query half space. Schipper and Overmars [143] give a technique for the planar case, by supporting weak deletions on the conjugation tree and then applying the global rebuilding...
Cited by: More
Geometric Range Searching - Matousek (1994) (Correct)
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BibTeX entry: (Update)
H. Schipper and M.H. Overmars, "Dynamic Partition Trees," Proc. SWAT'90, Lecture Notes in Computer Science 447 (1990), 404--417. http://citeseer.ist.psu.edu/schipper89dynamic.html More
@inproceedings{ schipper90dynamic,
author = "Haijo Schipper and Mark H. Overmars",
title = "Dynamic Partition Trees",
booktitle = "Scandinavian Workshop on Algorithm Theory",
pages = "404-417",
year = "1990",
url = "citeseer.ist.psu.edu/schipper89dynamic.html" }
Citations (may not include all citations):481 Algorithms in combinatorial geometry (context) - Edelsbrunner
106 Priority search trees (context) - McCreight - 1985
46 Decomposable searching problems (context) - Bentley - 1979
5 A deterministic algorithm for partitioning arrangements of l.. (context) - Agarwal - 1989
3 Intersection problems in computational geometry (context) - Edelsbrunner - 1982
2 Polytope range searching and integral geometry (context) - Chazelle - 1987
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