Computing Many Faces in Arrangements of Lines and Segments
Pankaj K. Agarwal, Jiřı́ Matoušek, Otfried Cheong Schwarzkopf · SIAM Journal on Computing · 1998
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 $O(n \log n)$ expected time algorithm for computing $\sqrt{n}$ cells in an arrangement of n lines.