Boundary Labeling: Models and Efficient Algorithms for Rectangular Maps

Bekos, Michael A.; Kaufmann, Michael; Symvonis, Antonios; Wolff, Alexander

doi:10.1007/978-3-540-31843-9_7

Cited by 48 publications

(126 citation statements)

References 12 publications

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“…They also showed that the problem of maximizing the size of the rectangular equal-width labels of the sites on a horizontal line with top or bottom edges coinciding with the input line under the 4S model can be solved in O(n 2 log n) time. Labeling where the labels are connected to their associated features by leaders has so far been studied in the map labeling literature by Bekos et al [4,5,7], Fekete and Plaisant [10], Freeman et al [12], Müller and Schödl [23] and Zoraster [29]. Our labeling model is quite similar to the boundary labeling model proposed by Bekos et al [7].…”

Section: Related Literaturementioning

confidence: 73%

“…Labeling where the labels are connected to their associated features by leaders has so far been studied in the map labeling literature by Bekos et al [4,5,7], Fekete and Plaisant [10], Freeman et al [12], Müller and Schödl [23] and Zoraster [29]. Our labeling model is quite similar to the boundary labeling model proposed by Bekos et al [7]. In boundary labeling, the labels are placed on the boundary of a rectangle R (referred to as enclosing rectangle), which encloses the set of sites, and they are connected to their associated sites by non-intersecting leaders.…”

Section: Related Literaturementioning

confidence: 99%

“…So, our problem can be easily formulated as a boundary labeling problem of minimum total leader length with non uniform sliding labels. Bekos et al [7] showed how to compute a legal boundary labeling of minimum total leader length in O(nW 2 ) time. 2…”

Section: Total Leader Length Minimizationmentioning

confidence: 99%

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Efficient Labeling of Collinear Sites

Bekos¹,

Kaufmann²,

Symvonis³

2008

JGAA

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In this paper we study the map labeling problem where the sites to be labeled are restricted to a line L. Previous models studied in the map labeling literature fail to produce label placements (i.e. place each label next to the site it describes) without label overlaps for certain instances of the problem with dense point sets. To address this problem, we propose a new approach according to which, given n sites each associated with an axis-parallel rectangular label, we aim to place the labels in distinct positions on the "boundary" of L so that they do not overlap and do not obscure the site set, and to connect each label with its associated site through a leader such that no two leaders intersect.We evaluate our labeling model under two minimization criteria: (i) total leader length and (ii) total number of leader bends. We show that both problems are N P -complete if the labels can be placed on both sides of L, while we present polynomial time algorithms for the case where the labels can be placed on only one side of L.

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Section: Related Literaturementioning

confidence: 73%

Section: Related Literaturementioning

confidence: 99%

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Efficient Labeling of Collinear Sites

Bekos¹,

Kaufmann²,

Symvonis³

2008

JGAA

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“…Boundary labeling was developed by Bekos et al [2] as a framework and an algorithmic response to the poor quality (feature occlusion, label overlap) of specific labeling applications. In boundary labeling, labels are placed at the boundary of a rectangle and are connected to their associated features via arcs referred to as leaders.…”

Section: Introductionmentioning

confidence: 99%

Many-to-One Boundary Labeling with Backbones

et al. 2013

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Abstract. In this paper we study many-to-one boundary labeling with backbone leaders. In this model, a horizontal backbone reaches out of each label into the feature-enclosing rectangle. Feature points associated with this label are linked via vertical line segments to the backbone. We present algorithms for label number and leader-length minimization. If crossings are allowed, we aim to minimize their number. This can be achieved efficiently in the case of fixed label order. We show that the corresponding problem in the case of flexible label order is NP-hard.

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“…Bekos et al use rectilinear leaders with up to two bends. They study settings with labels arranged on one, two, or four sides of the bounding box of the illustration [5], in multiple stacks to the left [3], or where the objects to be labeled are polygons rather than points [4]. The optimization criteria that they consider are minimizing the total length and minimizing the total number of bends.…”

Section: Introductionmentioning

confidence: 99%

Algorithms for Multi-Criteria Boundary Labeling

Benkert¹,

Haverkort²,

Kroll³

et al. 2009

JGAA

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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 crossing-free 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.

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Boundary Labeling: Models and Efficient Algorithms for Rectangular Maps

Cited by 48 publications

References 12 publications

Efficient Labeling of Collinear Sites

Efficient Labeling of Collinear Sites

Many-to-One Boundary Labeling with Backbones

Algorithms for Multi-Criteria Boundary Labeling

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