A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
The problem of compatible representatives
SIAM Journal on Discrete Mathematics
An empirical study of algorithms for point-feature label placement
ACM Transactions on Graphics (TOG)
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
OPT Versus LOAD in Dynamic Storage Allocation
SIAM Journal on Computing
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
IEEE Transactions on Visualization and Computer Graphics
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Adaptive zooming in point set labeling
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Dynamic one-sided boundary labeling
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
A zone-based approach for placing annotation labels on metro maps
SG'11 Proceedings of the 11th international conference on Smart graphics
Consistent labeling of rotating maps
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Information on the consequence of a move and its use for route improvisation support
COSIT'11 Proceedings of the 10th international conference on Spatial information theory
Approximation algorithms for free-label maximization
Computational Geometry: Theory and Applications
Approximation algorithms for free-label maximization
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Road segment selection with strokes and stability
Proceedings of the 1st ACM SIGSPATIAL International Workshop on MapInteraction
Consistent thinning of large geographical data for map visualization
ACM Transactions on Database Systems (TODS) - Invited papers issue
Spatially efficient design of annotated metro maps
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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Map labeling encounters unique issues in the context of dynamic maps with continuous zooming and panning-an application with increasing practical importance. In consistent dynamic map labeling, distracting behavior such as popping and jumping is avoided. We use a model for consistent dynamic labeling in which a label is represented by a 3d-solid, with scale as the third dimension. Each solid can be truncated to a single scale interval, called its active range, corresponding to the scales at which the label will be selected. The active range optimization (ARO) problem is to select active ranges so that no two truncated solids intersect and the sum of the heights of the active ranges is maximized. Simple ARO is a variant in which the active ranges are restricted so that a label is never deselected when zooming in. We investigate both the general and simple variants, for 1d- as well as 2d-maps. Different label shapes define different ARO variants. We show that 2d-ARO and general 1d-ARO are NP-complete, even for quite simple shapes. We solve simple 1d-ARO optimally with dynamic programming, and present a toolbox of algorithms that yield constant-factor approximations for a number of 1d- and 2d-variants.