Computational geometry: an introduction
Computational geometry: an introduction
Planar point location using persistent search trees
Communications of the ACM
Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Reporting and counting segment intersections
Journal of Computer and System Sciences
More on k-sets of finite sets in the plane
Discrete & Computational Geometry
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Sorting in c log n parallel steps
Combinatorica
Applications of random sampling in computational geometry, II
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Algorithms for diametral pairs and convex hulls that are optimal, randomized, and incremental
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A fast Las Vegas algorithm for triangulating a simple polygon
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Partition trees for triangle counting and other range searching problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
The complexity of many faces in arrangements of lines of segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Implicitly representing arrangements of lines or segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Ray shooting and other applications of spanning trees with low stabbing number
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Ray shooting and other applications of spanning trees with low stabbing number
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Cutting hyperplane arrangements
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Some new bounds for Epsilon-nets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
How to net a lot with little: small &egr;-nets for disks and halfspaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Stabbing and ray shooting in 3 dimensional space
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Intersection queries for curved objects (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Constructing arrangements optimally in parallel (preliminary version)
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Finding stabbing lines in 3-dimensional space
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Space-efficient ray-shooting and intersection searching: algorithms, dynamization, and applications
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Compact interval trees: a data structure for convex hulls
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Note: Computing closest and farthest points for a query segment
Theoretical Computer Science
| Hi-index | 0.01 |
In this paper we consider the following problem: Given a set ℒ of n lines in the plane, partition the plane into &Ogr;(r2) triangles so that no triangle intersects more than &Ogr;(n/r) lines of ℒ. We present a deterministic algorithm for this problem with &Ogr;(nr log n log&ohgr; r) running time, where &ohgr; is a constant r. In the second part of the paper, we apply this algorithm to several problems involving lines or segments in the plane, and obtain deterministic algorithms which are faster than any previously known algorithms. For example we give an &Ogr;(n2/3m2/3 log n log&ohgr;/3 m/√n + (m + n) log n) algorithm to compute all incidences between m points and n lines. Other problems include computing many faces in an arrangement of lines or segments, counting segment intersections, red-blue intersection detection, simplex range queries and computing stabbing trees with low stabbing number.