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Algorithms for MultiCriteria Boundary Labeling
, 2009
"... We present new algorithms for labeling a set P of n points in the plane with labels that are aligned to one side of the bounding box of P. The points are connected to their labels by curves (leaders) that consist of two segments: a horizontal segment, and a second segment at a fixed angle with the f ..."
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We present new algorithms for labeling a set P of n points in the plane with labels that are aligned to one side of the bounding box of P. The points are connected to their labels by curves (leaders) that consist of two segments: a horizontal segment, and a second segment at a fixed angle with the first. Our algorithms find a collection of crossingfree leaders that minimizes the total number of bends, the total length, or any other ‘badness ’ function of the leaders. A generalization to labels on two opposite sides of the bounding box of P is considered and an experimental evaluation of the performance is included. Submitted:
SYMVONIS A.: Combining traditional map labeling with boundary labeling
 In Proceedings of the 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM2011) (2011
"... Abstract. The traditional map labeling problems are mostly N Phard. Hence, effective heuristics and approximations have been developed in the past. Recently, efficient algorithms for the socalled boundary labeling model have been introduced which assumes that the labels are placed on the boundary ..."
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Abstract. The traditional map labeling problems are mostly N Phard. Hence, effective heuristics and approximations have been developed in the past. Recently, efficient algorithms for the socalled boundary labeling model have been introduced which assumes that the labels are placed on the boundary of the map and connected by polygonal leaders to their corresponding sites. Internal labels have been forbidden. In this paper, we allow both. Since clearly internal labels should be preferred, we consider several maximization problems for the number of internal labels and we show that they can be obtained efficiently or in quasipolynomial time.
AreaFeature Boundary Labeling
, 2009
"... Boundary labeling is a relatively new labeling method. It can be useful in automating the production of technical drawings and medical drawings, where it is common to explain certain parts of the drawing with text labels, arranged on its boundary so that other parts of the drawing are not obscured. ..."
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Boundary labeling is a relatively new labeling method. It can be useful in automating the production of technical drawings and medical drawings, where it is common to explain certain parts of the drawing with text labels, arranged on its boundary so that other parts of the drawing are not obscured. In boundary labeling, we are given a rectangle R which encloses a set of n sites. Each site s is associated with an axisparallel rectangular label ls. The labels must be placed in distinct positions on the boundary of R and they must be connected to their corresponding sites with polygonal lines, called leaders, so that the labels are pairwise disjoint and the leaders do not intersect each other. In this paper, we study a version of the boundary labeling problem where the sites can ‘float ’ within a polygonal region. We present a polynomial time algorithm, which runs in O(n 3) time and produces a labeling of minimum total leader length for labels of uniform size placed in fixed positions on the boundary of rectangle R.
Spatially Efficient Design of Annotated Metro Maps
"... Annotating metro maps with thumbnail photographs is a commonly used technique for guiding travelers. However, conventional methods usually suffer from small labeling space around the metro stations, especially when they are interchange stations served by two or more metro lines. This paper presents ..."
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Annotating metro maps with thumbnail photographs is a commonly used technique for guiding travelers. However, conventional methods usually suffer from small labeling space around the metro stations, especially when they are interchange stations served by two or more metro lines. This paper presents an approach for aesthetically designing schematic metro maps while ensuring effective placement of large annotation labels that are sufficiently close to their corresponding stations. Our idea is to distribute such labels in a wellbalanced manner to labeling regions around the metro network first and then adjust the lengths of metro line and leader line segments, which allows us to fully maximize the space coverage of the entire annotated map. This is accomplished by incorporating additional constraints into the conventional mixedinteger programming formulation, while we devised a threestep algorithm for accelerating the overall optimization process. We include several design examples to demonstrate the spatial efficiency of the map layout generated using the proposed approach through minimal user intervention.
Oneandahalfside Boundary Labeling
"... Abstract. In boundary labeling, each point site in a rectangular map is connected to a label outside the map by a leader, which may be a rectilinear or a straightline segment. Among various types of leaders, the socalled typeopo leader consists of three segments (from the site to its associated l ..."
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Abstract. In boundary labeling, each point site in a rectangular map is connected to a label outside the map by a leader, which may be a rectilinear or a straightline segment. Among various types of leaders, the socalled typeopo leader consists of three segments (from the site to its associated label) that are orthogonal, then parallel, and then orthogonal to the side to which the label is attached. In this paper, we investigate the socalled 1.5side boundary labeling, in which, in addition to being connected to the right side of the map directly, typeopo leaders can be routed to the left side temporarily and then finally to the right side. It turns out that allowing typeopo leaders to utilize the left side of a map is beneficial in the sense that it produces a better labeling result in some cases. To understand this new version of boundary labeling better, we investigate from a computational complexity viewpoint the total leader length minimization problem as well as the bend minimization problem for variants of 1.5side boundary labeling, which are parameterized by the underlying label size (uniform vs. nonuniform) and port type (fixed vs. sliding). For the case of nonuniform labels, the above two problems are intractable in general. We are able to devise pseudopolynomial time solutions for such intractable problems, and also identify the role played by the number of distinct labels in the overall complexity. On the other hand, if labels are identical in size, both problems become solvable in polynomial time. We also characterize the cases for which utilizing the left side for routing typeopo leaders does not help.
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
VoronoiBased Label Placement for Metro Maps
"... Metro maps with thumbnail photographs serve as common travel guides for providing sufficient information to meet the requirements of travelers in the cities. However, conventional methods attempt to minimize the total distance between stations and labels while maximizing the number of the labels ra ..."
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Metro maps with thumbnail photographs serve as common travel guides for providing sufficient information to meet the requirements of travelers in the cities. However, conventional methods attempt to minimize the total distance between stations and labels while maximizing the number of the labels rather than further taking into account the overall balance of the spatial distribution of labels. This paper presents an entropybased approach for effectively annotating large annotation labels sufficiently close to the metro stations. Our idea is to decompose the entire labeling space intro regions bounded by the metro lines, and then further partition each region into Voronoi cells, each of which is reserved for a station to be annotated. This is accomplished by incorporating a new geneticbased optimization, while the fitness of the decomposition is evaluated by the entropy of the relative coverage ratios of such Voronoi cells. We also include several design examples to demonstrate that the proposed approach successfully distributes large labels around the metro network with minimal user intervention. 1