Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Computing a face in an arrangement of line segments and related problems
SIAM Journal on Computing
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
SIAM Journal on Computing
Algorithmic geometry
Constructing Planar Cuttings in Theory and Practice
SIAM Journal on Computing
A Characterization of Planar Graphs by Pseudo-Line Arrangements
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
On-Line Zone Construction in Arrangements of Lines in the Plane
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
Dynamic Planar Convex Hull Operations in Near-Logarithmic Amortized Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximation algorithms for layered manufacturing
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
Online point location in planar arrangements and its applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Geometric algorithms for the analysis of 2D-electrophoresis gels
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Dynamic Planar Convex Hull with Optimal Query Time
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
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We present a randomized algorithm for computing portions of an arrangement of n arcs in the plane, each pair of which intersect in at most t points. We use this algorithm to perform online walks inside such an arrangement (i.e., compute all the faces that a curve, given in an online manner, crosses), and to compute a level in an arrangement, both in an output-sensitive manner. The expected running time of the algorithm is \math, where m is the number of intersections between the walk and the given arcs.No similarly efficient algorithm is known for the general case of arcs. For the case of lines and for certain restricted cases involving line segments, our algorithm improves the best known algorithm of [OvL81] by almost a logarithmic factor.