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Erschienen in:
2003 | OriginalPaper | Buchkapitel
On the Complexity of Many Faces in Arrangements of Pseudo-Segments and Circles
verfasst von : Pankaj K. Agarwal, Boris Aronov, Micha Sharir
Erschienen in: Discrete and Computational Geometry
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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We obtain improved bounds on the complexity of many faces in an arrangement of pseudo-segments, circles, or unit circles. The bounds are worst-case optimal for unit circles; they are also worst-case optimal for the case of pseudo-segments except when the number of faces is very small, in which case our upper bound is a polylogarithmic factor away from the best-known lower bound. For general circles, the bounds nearly coincide with the best-known bounds for the number of incidences between points and circles.