A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Label placement by maximum independent set in rectangles
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Point labeling with sliding labels
Computational Geometry: Theory and Applications - Special issue on applications and challenges
IEEE Transactions on Visualization and Computer Graphics
Fast point-feature label placement for dynamic visualizations
Information Visualization
Optimizing active ranges for consistent dynamic map labeling
Computational Geometry: Theory and Applications
Dynamic one-sided boundary labeling
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Approximation algorithms for free-label maximization
Computational Geometry: Theory and Applications
Road segment selection with strokes and stability
Proceedings of the 1st ACM SIGSPATIAL International Workshop on MapInteraction
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Dynamic maps that allow continuous map rotations, e.g., on mobile devices, encounter new issues unseen in static map labeling before. We study the following dynamic map labeling problem: The input is a static, labeled map, i.e., a set P of points in the plane with attached non-overlapping horizontal rectangular labels. The goal is to find a consistent labeling of P under rotation that maximizes the number of visible labels for all rotation angles such that the labels remain horizontal while the map is rotated. A labeling is consistent if a single active interval of angles is selected for each label such that labels neither intersect each other nor occlude points in P at any rotation angle. We first introduce a general model for labeling rotating maps and derive basic geometric properties of consistent solutions. We show NP-completeness of the active interval maximization problem even for unit-square labels. We then present a constant-factor approximation for this problem based on line stabbing, and refine it further into an EPTAS. Finally, we extend the EPTAS to the more general setting of rectangular labels of bounded size and aspect ratio.