Dynamic Point Labeling Is Strongly Pspace-Complete

Buchin, Kevin; Gerrits, Dirk H. P.

doi:10.1142/s0218195914600127

Cited by 7 publications

(6 citation statements)

References 9 publications

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“…If this was not the case, then the prefix [−M, 0] or the suffix [l 1 , l 1 + M] of K cannot belong to the activity of K . Further, for the interval [0, l 1 ] we obtain less than 2 3 M weight in total, because at most two labels can be active at the same time and l 1 < M 3 . Thus, we obtain W Φ < M + 2 3 M < 2M .…”

Section: Complexity Of K-restrictedmaxtotal In Am3mentioning

confidence: 99%

“…Further, for the interval [0, l 1 ] we obtain less than 2 3 M weight in total, because at most two labels can be active at the same time and l 1 < M 3 . Thus, we obtain W Φ < M + 2 3 M < 2M . On the other hand, because of l 2 ≥ 2M and W Φ ≥ W , we have W Φ ≥ 2M , which is a contradiction.…”

Section: Complexity Of K-restrictedmaxtotal In Am3mentioning

confidence: 99%

“…They present a sophisticated heuristic for finding a reasonable trade-off between label speed and label overlap. Finally, Buchin and Gerrits [2] show that dynamic point labeling is strongly PSPACE-complete.…”

Section: Introductionmentioning

confidence: 99%

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A Unified Model and Algorithms for Temporal Map Labeling

2020

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We consider map labeling for the case that a map undergoes a sequence of operations such as rotation, zoom and translation over a specified time span. We unify and generalize several previous models for dynamic map labeling into one versatile and flexible model. In contrast to previous research, we completely abstract from the particular operations and express the labeling problem as a set of time intervals representing the labels' presences, activities and conflicts. One of the model's strength is manifested in its simplicity and broad range of applications. In particular, it supports label selection both for map features with fixed position as well as for moving entities (e.g., for tracking vehicles in logistics or air traffic control). We study the active range maximization problem in this model. We prove that the problem is NPcomplete and W[1]-hard, and present constant-factor approximation algorithms. In the restricted, yet practically relevant case that no more than k labels can be active at any time, we give polynomial-time algorithms as well as constant-factor approximation algorithms.

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Section: Complexity Of K-restrictedmaxtotal In Am3mentioning

confidence: 99%

Section: Complexity Of K-restrictedmaxtotal In Am3mentioning

confidence: 99%

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A Unified Model and Algorithms for Temporal Map Labeling

2020

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“…Finally, we note that the dynamic problem has attracted attention in the past decade due to its increasing importance in several applications such as personal mapping systems. We refer to [2,[10][11][12]16,21,22] for problems with static sites and a dynamic map, and Buchin and Gerrits [3] for their hardness results. De Berg and Gerrits [7], on the other hand, discussed a trade-off between label speed and label overlap.…”

Section: Related Workmentioning

confidence: 99%

Minimum point-overlap labelling*

Higashikawa

Imai

Shiraga

et al. 2020

Optimization Methods and Software

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In an application of map labelling to air-traffic control, labels should be placed with as few overlaps as possible since labels include important information about airplanes. Motivated by this application, de Berg and Gerrits (Comput. Geom. 2012) proposed a problem of maximizing the number of free labels (i.e. labels not intersecting with any other label) and developed approximation algorithms for their problem under various label-placement models. In this paper, we propose an alternative problem of minimizing a degree of overlap at a point. Specifically, the objective of this problem is to minimize the maximum of λ(p) over p ∈ R 2 , where λ(p) is defined as the sum of weights of labels that overlap with a point p. We develop a 4-approximation algorithm by LP-rounding under the 4-position model. We also investigate the case when labels are rectangles with bounded height/length ratios.

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“…They presented a sophisticated heuristic for finding a reasonable trade-off between label speed and label overlap. Finally, Buchin and Gerrits [3] showed that dynamic point labeling is strongly PSPACE-complete. The corresponding viewport of the camera.…”

Section: Related Workmentioning

confidence: 99%

Temporal Map Labeling: A New Unified Framework with Experiments

Barth,

Niedermann,

Nöllenburg

et al. 2016

Preprint

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The increased availability of interactive maps on the Internet and on personal mobile devices has created new challenges in computational cartography and, in particular, for label placement in maps. Operations like rotation, zoom, and translation dynamically change the map over time and make a consistent adaptation of the map labeling necessary.In this paper, we consider map labeling for the case that a map undergoes a sequence of operations over a specified time span. We unify and generalize several preceding models for dynamic map labeling into one versatile and flexible model. In contrast to previous research, we completely abstract from the particular operations (e.g., zoom, rotation, etc.) and express the labeling problem as a set of time intervals representing the labels' presences, activities, and conflicts. The model's strength is manifested in its simplicity and broad range of applications. In particular, it supports label selection both for map features with fixed position as well as for moving entities (e.g., for tracking vehicles in logistics or air traffic control).Through extensive experiments on OpenStreetMap data, we evaluate our model using algorithms of varying complexity as a case study for navigation systems. Our experiments show that even simple (and thus, fast) algorithms achieve near-optimal solutions in our model with respect to an intuitive objective function.

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Dynamic Point Labeling Is Strongly Pspace-Complete

Cited by 7 publications

References 9 publications

A Unified Model and Algorithms for Temporal Map Labeling

A Unified Model and Algorithms for Temporal Map Labeling

Minimum point-overlap labelling*

Temporal Map Labeling: A New Unified Framework with Experiments

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