Elastic labels around the perimeter of a map

Iturriaga, Claudia; Lubiw, Anna

doi:10.1016/s0196-6774(03)00004-x

Cited by 12 publications

(4 citation statements)

References 5 publications

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“…A related problem has been considered by Iturriaga and Lubiw [14]. Given a set of n points on the boundary of a rectangle and for each point an elastic label of a certain area, they want to decide whether it is possible to attach these labels to their points inside the rectangle.…”

Section: Legal Leader-label Placementmentioning

confidence: 99%

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Boundary labeling: Models and efficient algorithms for rectangular maps

Bekos

Kaufmann

Symvonis

et al. 2007

Computational Geometry

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We introduce boundary labeling, a new model for labeling point sites with large labels. According to the boundary-labeling model, labels are placed around an axis-parallel rectangle that contains the point sites, each label is connected to its corresponding site through a polygonal line called leader, and no two leaders intersect. Although boundary labeling is commonly used, e.g., for technical drawings and illustrations in medical atlases, this problem has not yet been studied in the literature. The problem is interesting in that it is a mixture of a label-placement and a graph-drawing problem.In this paper we investigate several variants of the boundary-labeling problem. We consider labels of identical or different size, straight-line or rectilinear leaders, fixed or sliding ports for attaching leaders to sites and attaching labels to one, two or all four sides of the bounding rectangle. For any variant of the boundary labeling model, we aim at highly esthetical placements of labels and leaders. We present simple and efficient algorithms that minimize the total leader length or, in the case of rectilinear leaders, the total number of bends.

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Section: Legal Leader-label Placementmentioning

confidence: 99%

“…Iturriaga and Lubiw [14] give an O(n 4 )-time decision algorithm for attaching elastic labels to n sites on the perimeter of a rectangle. An elastic label models a block of text of fixed area, but varying width and height.…”

Section: Introductionmentioning

confidence: 99%

Boundary labeling: Models and efficient algorithms for rectangular maps

Bekos

Kaufmann

Symvonis

et al. 2007

Computational Geometry

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“…More recently, a broad family of anchored packing problems were proposed in the context of map labeling, where the anchors represent cities in a map, and axis-aligned rectangles represent labels [7,8,9,10,12,13,16]. Variants of the problem require the anchor to be at a corner, at a side, or anywhere in the rectangle, and the objective is to maximize the number of labels that can be packed in the map.…”

Section: Introductionmentioning

confidence: 99%

“…Many of these problems are known to be NP-complete. However, in all previous reductions, the label boxes have a finite number of possible sizes [7,12,16] or bounded size [8].…”

Section: Introductionmentioning

confidence: 99%

Maximum Area Axis-Aligned Square Packings

Akitaya,

Jones,

Stalfa

et al. 2018

Preprint

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Given a point set S = {s 1 , . . . , s n } in the unit square U = [0, 1] 2 , an anchored square packing is a set of n interior-disjoint empty squares in U such that s i is a corner of the ith square. The reach R(S) of S is the set of points that may be covered by such a packing, that is, the union of all empty squares anchored at points in S.It is shown that area(R(S)) ≥ 1 2 for every finite set S ⊂ U , and this bound is the best possible. The region R(S) can be computed in O(n log n) time. Finally, we prove that finding a maximum area anchored square packing is NP-complete. This is the first hardness proof for a geometric packing problem where the size of geometric objects in the packing is unrestricted.

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Boundary Labeling: Models and Efficient Algorithms for Rectangular Maps

et al. 2005

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Abstract. In this paper, we present boundary labeling, a new approach for labeling point sets with large labels. We first place disjoint labels around an axis-parallel rectangle that contains the points. Then we connect each label to its point such that no two connections intersect. Such an approach is common e.g. in technical drawings and medical atlases, but so far the problem has not been studied in the literature. The new problem is interesting in that it is a mixture of a label-placement and a graph-drawing problem.

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Elastic labels around the perimeter of a map

Cited by 12 publications

References 5 publications

Boundary labeling: Models and efficient algorithms for rectangular maps

Boundary labeling: Models and efficient algorithms for rectangular maps

Maximum Area Axis-Aligned Square Packings

Boundary Labeling: Models and Efficient Algorithms for Rectangular Maps

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