On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
When crossings count — approximating the minimum spanning tree
Proceedings of the sixteenth annual symposium on Computational geometry
Online point location in planar arrangements and its applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On the number of congruent simplices in a point
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Algorithms for center and Tverberg points
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Data structures for maintaining set partitions
Random Structures & Algorithms
Small-size ε-nets for axis-parallel rectangles and boxes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Near-linear approximation algorithms for geometric hitting sets
Proceedings of the twenty-fifth annual symposium on Computational geometry
A note about weak ε-nets for axis-parallel boxes in d-space
Information Processing Letters
Small-Size $\eps$-Nets for Axis-Parallel Rectangles and Boxes
SIAM Journal on Computing
Semialgebraic Range Reporting and Emptiness Searching with Applications
SIAM Journal on Computing
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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.