Abstract
We prove the existence of linear size binary space partitions for sets of objects in the plane under certain conditions that are often satisfied in practical situations. In particular, we construct linear size binary space partitions for sets of fat objects, for sets of line segments where the ratio between the lengths of the longest and shortest segment is bounded by a constant, and for homothetic objects. For all cases we also show how to turn the existence proofs into efficient algorithms.
Supported by the Dutch Organisation for Scientific Research (N.W.O.) and by ESPRIT Basic Research Action No. 7141 (project ALCOM II: Algorithms and Complexity)
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© 1994 Springer-Verlag Berlin Heidelberg
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de Berg, M., de Groot, M., Overmars, M. (1994). New results on binary space partitions in the plane (extended abstract). In: Schmidt, E.M., Skyum, S. (eds) Algorithm Theory — SWAT '94. SWAT 1994. Lecture Notes in Computer Science, vol 824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58218-5_6
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DOI: https://doi.org/10.1007/3-540-58218-5_6
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