Optimizing active ranges for consistent dynamic map labeling

Been, Ken; Nöllenburg, Martin; Poon, Sheung-Hung; Wolff, Alexander

doi:10.1145/1377676.1377681

Cited by 20 publications

(27 citation statements)

References 11 publications

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“…Been et al [25] considered the case that a user changes the scale of the map by zooming in or out and, at any time, a conflict-free set of labels has to be presented. In this scenario, it is undesirable that labels flicker on and off, thus every label is allowed to be visible only in a single continuous range of scales, which is termed the label's active range.…”

Section: Related Workmentioning

confidence: 99%

Beyond Maximum Independent Set: An Extended Integer Programming Formulation for Point Labeling

Haunert

Wolff

2017

IJGI

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Map labeling is a classical problem of cartography that has frequently been approached by combinatorial optimization. Given a set of features in a map and for each feature a set of label candidates, a common problem is to select an independent set of labels (that is, a labeling without label-label intersections) that contains as many labels as possible and at most one label for each feature. To obtain solutions of high cartographic quality, the labels can be weighted and one can maximize the total weight (rather than the number) of the selected labels. We argue, however, that when maximizing the weight of the labeling, the influences of labels on other labels are insufficiently addressed. Furthermore, in a maximum-weight labeling, the labels tend to be densely packed and thus the map background can be occluded too much. We propose extensions of an existing model to overcome these limitations. Since even without our extensions the problem is NP-hard, we cannot hope for an efficient exact algorithm for the problem. Therefore, we present a formalization of our model as an integer linear program (ILP). This allows us to compute optimal solutions in reasonable time, which we demonstrate both for randomly generated point sets and an existing data set of cities. Moreover, a relaxation of our ILP allows for a simple and efficient heuristic, which yielded near-optimal solutions for our instances.

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Section: Related Workmentioning

confidence: 99%

Beyond Maximum Independent Set: An Extended Integer Programming Formulation for Point Labeling

Haunert

Wolff

2017

IJGI

Self Cite

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“…Been et al [3] treated the problems of maximizing sum of active ranges, where the active range of a label is a contiguous range of the map scales at which is displayed. Moreover, these problems require that the labels are pairwise disjoint at any scale and satisfy the consistency desiderata.…”

Section: Related Workmentioning

confidence: 99%

“…There are many dynamic cases, involving for example, panning, rotating, and zooming maps, translating points, moving points with different velocities. In this context, studies on map label- imai@ise.chuo-u.ac.jp ing for dynamic cases have been presented in which mainly the dynamic label number maximization problem has been considered [2], [3], [5], [10], [11], [12], [13], [15], [25]. However, for dynamic maps, there are not many studies for label size maximization problem [16].…”

Section: Introductionmentioning

confidence: 99%

Polynomial Time Algorithms for Label Size Maximization on Rotating Maps

Yokosuka

Imai

2017

Journal of Information Processing

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Map labeling is the problem of placing labels at corresponding graphical features on a map. There are two main optimization problems: the label number maximization problem and the label size maximization problem. In general, both problems are NP-hard for static maps. Recently, the widespread use of several applications, such as personal mapping systems, has increased the importance of dynamic maps and the label number maximization problem for dynamic cases has been studied. In this paper, we consider the label size maximization problem for points on rotating maps. Our model is as follows. For each label, an anchor point is chosen inside the label or on its boundary. Each label is placed such that the anchor point coincides with the corresponding point on the map. Furthermore, while the map fully rotates from 0 to 2π, the labels are placed horizontally according to the angle of the map. Our problem consists of finding the maximum scale factor for the labels such that the labels do not intersect, and determining the placing of the anchor points. We describe an O(n log n)-time and O(n)-space algorithm for the case where each anchor point is inside the label. Moreover, if the anchor points are on the boundaries, we also present an O(n log n)-time and O(n)-space exact and approximation algorithms for several label shapes.

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“…During zooming (and panning) the users should not be confronted with shocks in the label display. In Been et al (2010) this is called the 'Dynamic Map Labeling' problem and the paper also applies the paradigm that scale is considered as additional dimension (as in our smooth tGAP represented by the SSC). We want to further explore how their smooth label approach fits in our SSC.…”

Section: Open Research Questionsmentioning

confidence: 99%