Computational geometry: an introduction
Computational geometry: an introduction
A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A rule-based system for dense-map name placement
Communications of the ACM
The problem of compatible representatives
SIAM Journal on Discrete Mathematics
Approximate map labeling is in &OHgr;(n log n)
Information Processing Letters
An empirical study of algorithms for point-feature label placement
ACM Transactions on Graphics (TOG)
Map labeling heuristics: provably good and practically useful
Proceedings of the eleventh annual symposium on Computational geometry
A unified approach to labeling graphical features
Proceedings of the fourteenth annual symposium on Computational geometry
A polynomial time solution for labeling a rectilinear map
Information Processing Letters
Label placement by maximum independent set in rectangles
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Map labeling and its generalizations
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Point labeling with sliding labels
Computational Geometry: Theory and Applications - Special issue on applications and challenges
Point set labeling with specified positions
Proceedings of the sixteenth annual symposium on Computational geometry
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Cartographic Name Placement with Prolog
IEEE Computer Graphics and Applications
Static and Dynamic Algorithms for k-Point Clustering Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Efficient Approximation Algorithms for Multi-label Map Labeling
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
A Better Lower Bound for Two-Circle Point Labeling
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
An Algorithm for Labeling Edges of Hierarchical Drawings
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Elastic Labels: the Two-Axis Case
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
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In this paper, we present an O(n3 log n) time solution for the following multi-label map labeling problem: Given a set S of n distinct sites in the plane, place at each site a triple of uniform squares of maximum possible size such that all the squares are axis-parallel and a site is on the boundaries of its three labeling squares. We also study the problem under the discrete model, i.e., a site must be at the corners of its three label squares. We obtain an optimal θ(n log n) time algorithm for the latter problem.