A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
An efficient algorithm for finding a maximum weight 2-independent set on interval graphs
Information Processing Letters
An empirical study of algorithms for point-feature label placement
ACM Transactions on Graphics (TOG)
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
Practical extensions of point labeling in the slider model
Proceedings of the 7th ACM international symposium on Advances in geographic information systems
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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Annotating maps, graphs, and diagrams with pieces of text is an important step in information visualization that is usually referred to as label placement. We define nine label-placement models for labeling points with axis-parallel rectangles given a weight for each point. There are two groups; fixed-position models and slider models. We aim to maximize the weight sum of those points that receive a label. We first compare our models by giving bounds for the ratios between the weights of maximum-weight labelings in different models. Then we present algorithms for labeling n points with unit-height rectangles. We show how an O(n log n)-time factor-2 approximation algorithm and a PTAS for fixed-position models can be extended to handle the weighted case. Our main contribution is the first algorithm for weighted sliding labels. Its approximation factor is (2 + Ɛ), it runs in O(n2/Ɛ) time and uses O(n/Ɛ) space. We also investigate some special cases.