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COMPGEOM
1991
ACM

Arrangements of Segments that Share Endpoints: Single Face Results

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Arrangements of Segments that Share Endpoints: Single Face Results
We provide new combinatorial bounds on the complexity of a face in an arrangement of segments in the plane. In particular, we show that the complexity of a single face in an arrangement of n line segments determined by h endpoints is O(hlogh). While the previous upper bound, O(n (n)), is tight for segments with distinct endpoints, it is far from being optimal when n = (h2 ). Our result shows that, in a sense, the fundamental combinatorial complexity of a face arises not as a result of the number of segments, but rather as a result of the number of endpoints.
Esther M. Arkin, Dan Halperin, Klara Kedem, Joseph
Added 27 Aug 2010
Updated 27 Aug 2010
Type Conference
Year 1991
Where COMPGEOM
Authors Esther M. Arkin, Dan Halperin, Klara Kedem, Joseph S. B. Mitchell, Nir Naor
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