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 polynomial time solution for labeling a rectilinear map
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A practical map labeling algorithm
Computational Geometry: Theory and Applications
Label placement by maximum independent set in rectangles
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Labeling a rectilinear map more efficiently
Information Processing Letters
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
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Label updating to avoid point-shaped obstacles in fixed model
Theoretical Computer Science
Incremental labeling in closed-2PM model
Computers and Electrical Engineering
Adaptive zooming in point set labeling
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We investigate a special class of map labeling problem. Let P = {p1, p2, ..., pn} be a set of point sites distributed on a 2D map. A label associated with each point is a axis-parallel rectangle of a constant height but of variable width.Here height of a label indicates the font size and width indicates the number of characters in that label. For a point pi, its label contains the point pi at its top-left or bottom-left corner, and it does not obscure any other point in P. Width of the label for each point in P is known in advance.The objective is to label the maximum number of points on the map so that the placed labels are mutually nonoverlapping. We first consider a simple model for this problem. Here, for each point pi, the corner specification (i.e., whether the point pi would appear at the top-left or bottom-left corner of the label) is known. We formulate this problem as finding the maximum independent set of a chordal graph, and propose an O(nlogn) time algorithm for producing the optimal solution.If the corner specification of the points in P is not known, our algorithm is a 2-approximation algorithm.Next, we develop a good heuristic algorithm that is observed to produce optimal solutions for most of the randomly generated instances and for all the standard benchmarks available in [13].