Labeling Subway Lines

Garrido, Miguel Ángel Mesa; Iturriaga, Claudia; Márquez, Alberto; Portillo, José R.; Reyes, Pedro de los; Wolff, Alexander

doi:10.1007/3-540-45678-3_55

Cited by 17 publications

(20 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The problem of labeling points on a single line has so far been studied by Garrido et al [14] and Chen et al [9], along two different labeling models: 4P and 4S. In the fixed-position model 4P a label must be placed so that the site to be labeled coincides with one of its four corners 2 (see Figure 3), whereas in the sliding model 4S a label can be placed so that the site lies on one of the boundary edges of the label 3 ( Figure 4 illustrates the 4S model, where the label can be shifted continuously as indicated by the arrows).…”

Section: Related Literaturementioning

confidence: 99%

See 1 more Smart Citation

Efficient Labeling of Collinear Sites

Bekos¹,

Kaufmann²,

Symvonis³

2008

JGAA

View full text Add to dashboard Cite

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.

show abstract

Section: Related Literaturementioning

confidence: 99%

“…We will reduce the problem of determining a legal labeling under the 1d-4S sliding model, which is known to be N P -complete [14], to our problem. Recall that in 1d-4S, all sites lie on a horizontal line and each label must be placed, so that the site lies on one of the boundary edges of the label.…”

Section: Total Leader Length Minimizationmentioning

confidence: 99%

Efficient Labeling of Collinear Sites

Bekos¹,

Kaufmann²,

Symvonis³

2008

JGAA

View full text Add to dashboard Cite

show abstract

“…Since this problem in general is known to be NP-complete, many heuristics or special cases for which polynomial time algorithms are given have been presented. For instance, there are many algorithms that have been developed for labeling points that are on lines [5,9,11,12,19,22] or in a region [7,8,13,14,15,16,17,18,20,21].…”

Section: Introductionmentioning

confidence: 99%

“…This problem has been studied previously [9,16,19,5]. The prefix 1d or Slope refers to the problem in which the anchors lie on a horizontal or a sloping line, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…The prefix 1d or Slope refers to the problem in which the anchors lie on a horizontal or a sloping line, respectively. Garrido et al [9] gave linear time algorithms for 1d4P rectangle label, 1d4S square label, and Slope4P square label models, and a quadratic time algorithm for Slope4S square label model as well. They also showed 1d4S rectangle label is NP-complete and consider the maximization version to maximize the size of labels.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Maximizing the Number of Independent Labels in the Plane

Liao

Lee

Frontiers in Algorithmics

View full text Add to dashboard Cite

Abstract. In this paper, we consider a map labeling problem to maximize the number of independent labels in the plane. We first investigate the point labeling model that each label can be placed on a given set of anchors on a horizontal line. It is known that most of the map labeling decision models on a single line (horizontal or slope line) can be easily solved. However, the label number maximization models are more difficult (like 2SAT vs. MAX-2SAT). We present an O(n log Δ) time algorithm for the four position label model on a horizontal line based on dynamic programming and a particular analysis, where n is the number of the anchors and Δ is the maximum number of labels whose intersection is nonempty. (1 + 1/k)-factor PTAS algorithms that run in O(n log n + n 2k−1 ) time and O(n log n + nΔ k−1 ) time respectively for the fixed-height rectangle label placement model in the plane, we extend our method to improve their algorithms and present a (1 + 1/k)-factor PTAS algorithm that runs in O(n log n + kn log 4 Δ + Δ k−1 ) time using O(kΔ 3 log 4 Δ + kΔ k−1 ) storage.

show abstract

Periodic Multi-labeling of Public Transit Lines

Polishchuk

Vihavainen

2010

Geographic Information Science

View full text Add to dashboard Cite

Labeling Subway Lines

Cited by 17 publications

References 13 publications

Efficient Labeling of Collinear Sites

Efficient Labeling of Collinear Sites

Maximizing the Number of Independent Labels in the Plane

Periodic Multi-labeling of Public Transit Lines

Contact Info

Product

Resources

About