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Twosided boundary labeling with adjacent sides. Arxiv report, Apr. 2013. Available at http://arxiv.org/abs/TODO
"... Abstract In the Boundary Labeling problem, we are given a set of n points, referred to as sites, inside an axisparallel rectangle R, and a set of n pairwise disjoint rectangular labels that are attached to R from the outside. The task is to connect the sites to the labels by nonintersecting polygo ..."
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Abstract In the Boundary Labeling problem, we are given a set of n points, referred to as sites, inside an axisparallel rectangle R, and a set of n pairwise disjoint rectangular labels that are attached to R from the outside. The task is to connect the sites to the labels by nonintersecting polygonal paths, socalled leaders. In this paper, we study the TwoSided Boundary Labeling with Adjacent Sides problem, with labels lying on two adjacent sides of the enclosing rectangle. We restrict ourselves to rectilinear leaders with at most one bend. We present a polynomialtime algorithm that computes a crossingfree leader layout if one exists. So far, such an algorithm has only been known for the simpler cases that labels lie on one side or on two opposite sides of R (where a crossingfree solution always exists).
Shooting Bricks with Orthogonal Laser Beams: A First Step towards Internal/External Map Labeling
"... We study several variants of a hybrid map labeling problem that combines the following two tasks: (i) a set A of points in a rectangle R needs to be labeled with rectangular labels on the right boundary of R using rectilinear onebend polylines called leaders to connect points and labels; (ii) a max ..."
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We study several variants of a hybrid map labeling problem that combines the following two tasks: (i) a set A of points in a rectangle R needs to be labeled with rectangular labels on the right boundary of R using rectilinear onebend polylines called leaders to connect points and labels; (ii) a maximum subset B ′ of a set B of fixed internal congruent rectangular labels in R needs to be selected such that B ′ is an independent set of labels and no leader intersects any label in B ′. We also call the points in A aliens, the labels of B bricks, and the leaders laser beams. Then the problem translates into every alien shooting a laser beam so that in total as few bricks as possible are destroyed. We provide algorithms and NPhardness results for different variants of the problem. 1
MultiSided Boundary Labeling
"... In the Boundary Labeling problem, we are given a set of n points, referred to as sites, inside an axisparallel rectangle R, and a set of n pairwise disjoint rectangular labels that are attached to R from the outside. The task is to connect the sites to the labels by nonintersecting rectilinear pat ..."
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In the Boundary Labeling problem, we are given a set of n points, referred to as sites, inside an axisparallel rectangle R, and a set of n pairwise disjoint rectangular labels that are attached to R from the outside. The task is to connect the sites to the labels by nonintersecting rectilinear paths, socalled leaders, with at most one bend. In this paper, we study the MultiSided Boundary Labeling problem, with labels lying on at least two sides of the enclosing rectangle. We present a polynomialtime algorithm that computes a crossingfree leader layout if one exists. So far, such an algorithm has only been known for the cases that labels lie on one side or on two opposite sides of R (where a crossingfree solution always exists). For the more difficult case where labels lie on adjacent sides, we show how to compute crossingfree leader layouts that maximize the number of labeled points or minimize the total leader length. 1