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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Vydané v:	Applied mathematics and computation Ročník 309; s. 359 - 373
Hlavní autori:	Claverol, Mercè, Garijo, Delia, Korman, Matias, Seara, Carlos, Silveira, Rodrigo I.
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 15.09.2017
Predmet:	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
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Popis
Shrnutí:	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