Online point location in planar arrangements and its applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Point-line incidences in space
Proceedings of the eighteenth annual symposium on Computational geometry
Improved construction of vertical decompositions of three-dimensional arrangements
Proceedings of the eighteenth annual symposium on Computational geometry
Motorcycle graphs and straight skeletons
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Pseudo-line arrangements: duality, algorithms, and applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Taking a Walk in a Planar Arrangement
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Point–Line Incidences in Space
Combinatorics, Probability and Computing
Linear-time algorithms for geometric graphs with sublinearly many crossings
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings
SIAM Journal on Computing
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We present several variants of a new randomized incremental algorithm for computing a cutting in an arrangement of n lines in the plane. The algorithms produce cuttings whose expected size is O(r2), and the expected running time of the algorithms is O(nr). Both bounds are asymptotically optimal for nondegenerate arrangements. The algorithms are also simple to implement, and we present empirical results showing that they perform well in practice. We also present another efficient algorithm (with slightly worse time bound) that generates small cuttings whose size is guaranteed to be close to the best known upper bound of J. Matou{s}ek [Discrete Comput. Geom., 20 (1998), pp. 427--448].