Computing many faces in arrangements of lines and segments

Authors:
Pankaj K. Agarwal;Jiří Matoušek;Otfried Schwarzkopf
Affiliations:
Department of Computer Science, Box 90129, Duke University, Durham, NC;Department of Applied Mathematics, Charles University, Malostranskéńm. 25, 118 00 Praha 1, Czech Republic;Department of Computer Science, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, the Netherlands
Venue:
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Year:
1994

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Abstract

We present randomized algorithms for computing many faces in an arrangement of lines or of segments in the plane, which are considerably simpler and slightly faster than the previously known ones. The main new idea is a simple randomized O(nlogn) expected time algorithm for computing n cells in an arrangement of n lines.