Efficient algorithms for geometric graph search problems
SIAM Journal on Computing
A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A Factor-2 Approximation for Labeling Points with Maximum Sliding Labels
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
A Combinatorial Framework for Map Labeling
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Matching points with rectangles and squares
Computational Geometry: Theory and Applications
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In this paper, we consider the following problem: Given n pairs of a point and an axis-parallel rectangle in the plane, place each rectangle at each point in order that the point lies on the corner of the rectangle and the rectangles do not intersect. If the size of the rectangles may be enlarged or reduced at the same factor, maximize the factor. This paper generalizes the results of Formann and Wagner [Proc. 7th Annual ACM Symp. on Comput. Geometry (SoCG'91), 1991, pp. 281-288]. They considered the uniform squares case and showed that there is no polynomial time algorithm less than 2-approximation. We present a 2- approximation algorithm of the non-uniform rectangle case which runs in O(n2 log n) time and takes O(n2) space. We also show that the decision problem can be solved in O(n logn) time and space in the RAM model by transforming file problem to a simpler geometric problem.