Applied mathematics and computation

Vol. 309, p. 359-373

DOI: 10.1016/j.amc.2017.04.001

Date of publication: 2017-09-15

Abstract:

Given a set S of n line segments in the plane, we say that a region R ¿ R 2 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(n log n) (for strips, quadrants, and 3-sided rectangles), and O(n2 log n) (for rectangles).

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).]]>

Spanish Meeting on Computational Geometry

p. 61-64

Presentation's date: 2017-06-26

Abstract:

In this work we study the metric dimension and the location-domination number of maximal outerplanar graphs. Concretely, we determine tight upper and lower bounds on the metric dimension and characterize those maximal outerplanar graphs attaining the lower bound. We also give a lower bound on the location-domination number of maximal outerplanar graphs.]]>