On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Fat triangles determine linearly many holes
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Arrangements of curves in the plane—topology, combinatorics, and algorithms
Theoretical Computer Science
Counting and cutting cycles of lines and rods in space
Computational Geometry: Theory and Applications
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
Computing a face in an arrangement of line segments and related problems
SIAM Journal on Computing
Computing and Verifying Depth Orders
SIAM Journal on Computing
On joints in arrangements of lines in space and related problems
Journal of Combinatorial Theory Series A
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Cutting cylces of rods in space
Proceedings of the fourteenth annual symposium on Computational geometry
Computing Many Faces in Arrangements of Lines and Segments
SIAM Journal on Computing
Algorithmic geometry
Spanning trees crossing few barriers
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
When crossings count — approximating the minimum spanning tree
Proceedings of the sixteenth annual symposium on Computational geometry
Constructing Planar Cuttings in Theory and Practice
SIAM Journal on Computing
Reporting Red-Blue Intersections between Two Sets of Connected Line Segments
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Dynamic Planar Convex Hull Operations in Near-Logarithmic Amortized Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Taking a Walk in a Planar Arrangement
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Segment intersection searching problems in general settings
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Reporting Intersecting Pairs of Polytopes in Two and Three Dimensions
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
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Recently, Har-Peled [17] presented a new randomized technique for online construction of the zone of a curve in a planar arrangement of arcs. In this paper: we present several applications of this technique, which yield improved solutions to a variety of problems. These applications include: (i) an efficient mechanism for performing online point location queries in an arrangement of arcs; (ii) an efficient algorithm for computing an approximation to the minimum-weight Steiner-tree of a set of points, where the weight is the number of intersections between the tree edges and a given collection of arcs; (iii) a subquadratic algorithm for cutting a set of pseudo-parabolas into pseudo-segments; (iv) an algorithm for cutting a set of line segments (`rods') in 3-space so as to eliminate all cycles in the vertical depth order; and (v) a near-optimal algorithm for reporting all bichromatic intersections between a set R of red arcs and a set B of blue arcs, where the unions of the arcs in each set are both connected.