Stabbing segments with rectilinear objects

Given a set S of n line segments in the plane, we say that a region R⊆R2 is a stabber for S if R contains exactly one endpoint of each segment of S. In this paper we provide optimal or near-optimal algorithms for reporting all combinatorially different stabbers for several shapes of stabbers. Specif...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 309; pp. 359 - 373
Main Authors: Claverol, Mercè, Garijo, Delia, Korman, Matias, Seara, Carlos, Silveira, Rodrigo I.
Format: Journal Article Publication
Language:English
Published: Elsevier Inc 15.09.2017
Subjects:
68 Computer science
68W Algorithms
Algorismes
Algorithms
Classificació AMS
Classification problems
Computational geometry
Geometria computacional
Line segments
Matemàtiques i estadística
Stabbing problems
Àrees temàtiques de la UPC
Computational geometry
Line segments
Algorithms
Stabbing problems
Classification problems
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:Given a set S of n line segments in the plane, we say that a region R⊆R2 is a stabber for S if R contains exactly one endpoint of each segment of S. In this paper we provide optimal or near-optimal algorithms for reporting all combinatorially different stabbers for several shapes of stabbers. Specifically, we consider the case in which the stabber can be described as the intersection of axis-parallel halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). The running times are O(n) (for the halfplane case), O(nlog n) (for strips, quadrants, and 3-sided rectangles), and O(n2log n) (for rectangles).
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2017.04.001