Computational geometry: an introduction
Computational geometry: an introduction
Toughness and Delaunay triangulations
Discrete & Computational Geometry
A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Lower bounds for algebraic computation trees with integer inputs
SIAM Journal on Computing
The problem of compatible representatives
SIAM Journal on Discrete Mathematics
Reconstructing sets of orthogonal line segments in the plane
Discrete Mathematics
A polynomial time solution for labeling a rectilinear map
Information Processing Letters
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
On a matching problem in the plane
Discrete Mathematics
Polynomial time algorithms for three-label point labeling
Theoretical Computer Science - Computing and combinatorics
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Labeling points with given rectangles
Information Processing Letters
Boundary labeling: Models and efficient algorithms for rectangular maps
Computational Geometry: Theory and Applications
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Journal of Computer and System Sciences
New bounds on map labeling with circular labels
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Non-crossing matchings of points with geometric objects
Computational Geometry: Theory and Applications
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In this paper we deal with the following natural family of geometric matching problems. Given a class C of geometric objects and a set P of points in the plane, a C-matching is a set M@?C such that every C@?M contains exactly two elements of P. The matching is perfect if it covers every point, and strong if the objects do not intersect. We concentrate on matching points using axes-aligned squares and rectangles. We propose an algorithm for strong rectangle matching that, given a set of n points, matches at least 2@?n/3@? of them, which is worst-case optimal. If we are given a combinatorial matching of the points, we can test efficiently whether it has a realization as a (strong) square matching. The algorithm behind this test can be modified to solve an interesting new point-labeling problem. On the other hand we show that it is NP-hard to decide whether a point set has a perfect strong square matching.