Abstract
Every set S of n points in the plane has a spanning tree such that no line disjoint from S has more than O(√n) intersections with the tree (where the edges are embedded as straight line segments). We review the proof of this result (originally proved by Bernard Chazelle and the author in a more general setting), point at some methods for constructing such a tree, and describe some algorithmic and combinatorial applications.
Supported by the Deutsche Forschungsgemeinschaft, “Schwerpunktprogramm Datenstrukturen und effiziente Algorithmen”, grant We 1265/1-2.
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© 1992 Springer-Verlag Berlin Heidelberg
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Welzl, E. (1992). On spanning trees with low crossing numbers. In: Monien, B., Ottmann, T. (eds) Data structures and efficient algorithms. Lecture Notes in Computer Science, vol 594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55488-2_30
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DOI: https://doi.org/10.1007/3-540-55488-2_30
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