Abstract
In this paper we deal with the following natural family of geometric matching problems. Given a class \({\mathcal C}\) of geometric objects and a point set P, a \({\mathcal C}\)-matching is a set M \(\subseteq {\mathcal C}\) 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 axis-aligned squares and rectangles. We give algorithms for these classes and show that it is NP-hard to decide whether a point set has a perfect strong square matching. We show that one of our matching algorithms solves a family of map-labeling problems.
Work supported by grant WO 758/4-2 of the German Science Foundation (DFG).
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Bereg, S., Mutsanas, N., Wolff, A. (2006). Matching Points with Rectangles and Squares. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_15
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DOI: https://doi.org/10.1007/11611257_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31198-0
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