Data structures and network algorithms
Data structures and network algorithms
Computational geometry: an introduction
Computational geometry: an introduction
Principles of interactive computer graphics (2nd ed.)
Principles of interactive computer graphics (2nd ed.)
Reporting and counting segment intersections
Journal of Computer and System Sciences
Sorting Jordan sequences in linear time using level-linked search trees
Information and Control
Computing convolutions by reciprocal search
SCG '86 Proceedings of the second annual symposium on Computational geometry
Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Algorithms
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
Applications of random sampling in computational geometry, II
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Plane-sweep algorithms for intersecting geometric figures
Communications of the ACM
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
An optimal algorithm for the (≤ k)-levels, with applications to separation and transversal problems
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Decision trees for geometric models
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Vertical decompositions for triangles in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
GASP: a system to facilitate animating geometric algorithms
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On point location and motion planning among simplices
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Rounding arrangements dynamically
Proceedings of the eleventh annual symposium on Computational geometry
An optimal algorithm for finding segments intersections
Proceedings of the eleventh annual symposium on Computational geometry
Computing the visibility graph via pseudo-triangulations
Proceedings of the eleventh annual symposium on Computational geometry
Computing faces in segment and simplex arrangements
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Simple and practical geometric algorithms
ACM Computing Surveys (CSUR) - Special issue: position statements on strategic directions in computing research
Randomized external-memory algorithms for some geometric problems
Proceedings of the fourteenth annual symposium on Computational geometry
An exact interactive time visibility ordering algorithm for polyhedral cell complexes
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Efficient algorithms for line and curve segment intersection using restricted predicates
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
On degeneracy in geometric computations
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Computing the arrangement of curve segments: divide-and-conquer algorithms via sampling
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Visualization of Geometric Algorithms
IEEE Transactions on Visualization and Computer Graphics
Reporting intersecting pairs of convex polytopes in two and three dimensions
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Reporting intersections among thick objects
Information Processing Letters
Improved Optimal Weighted Links Algorithms
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Parallel Optimal Weighted Links
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Reporting Intersecting Pairs of Polytopes in Two and Three Dimensions
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Structure Theorems for Systems of Segments
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Intersecting Red and Blue Line Segments in Optimal Time and Precision
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Simple and Efficient Bilayer Cross Counting
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Decomposable multi-parameter matroid optimization problems
Theoretical Computer Science - Latin American theoretical informatics
Route planning and map inference with global positioning traces
Computer Science in Perspective
GASP: a system for visualizing geometric algorithms
VIS '94 Proceedings of the conference on Visualization '94
Testing bipartiteness of geometric intersection graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Managing uncertainty in moving objects databases
ACM Transactions on Database Systems (TODS)
Algorithms for the placement of diagrams on maps
Proceedings of the 12th annual ACM international workshop on Geographic information systems
Detecting tetrahedralizations of a set of line segments
Journal of Algorithms
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
ACM Transactions on Database Systems (TODS)
An intersection-sensitive algorithm for snap rounding
Computational Geometry: Theory and Applications
An algorithm for polygon clipping, and for determining polygon intersections and unions
Computers & Geosciences
A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums
Computers and Operations Research
Line-segment intersection made in-place
Computational Geometry: Theory and Applications
Randomized Algorithms for Minimum Distance Localization
International Journal of Robotics Research
SIGITE '08 Proceedings of the 9th ACM SIGITE conference on Information technology education
Relative Convex Hulls in Semi-dynamic Subdivisions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Topological sweep of the complete graph
Discrete Applied Mathematics
Linear-time algorithms for geometric graphs with sublinearly many crossings
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Testing bipartiteness of geometric intersection graphs
ACM Transactions on Algorithms (TALG)
Parallel Optimal Weighted Links
Transactions on Computational Science III
Optimal higher order Delaunay triangulations of polygons
Computational Geometry: Theory and Applications
Optimal in-place algorithms for 3-D convex hulls and 2-D segment intersection
Proceedings of the twenty-fifth annual symposium on Computational geometry
Counting and representing intersections among triangles in three dimensions
Computational Geometry: Theory and Applications
A parallel plane sweep algorithm for multi-core systems
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Algorithms for memory hierarchies: advanced lectures
Algorithms for memory hierarchies: advanced lectures
Red-blue separability problems in 3D
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Optimal higher order Delaunay triangulations of polygons
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Optimal in-place and cache-oblivious algorithms for 3-d convex hulls and 2-d segment intersection
Computational Geometry: Theory and Applications
Guaranteeing safety in spatially situated agents
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Algorithms and theory of computation handbook
Efficient view point selection for silhouettes of convex polyhedra
Computational Geometry: Theory and Applications
Convex hull of imprecise points in o(n log n) time after preprocessing
Proceedings of the twenty-seventh annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings
SIAM Journal on Computing
Geospatial overlay computation on the GPU
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Algorithms for vector graphic optimization and compression
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
Fault tolerant guarding of grids
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Every graph admits an unambiguous bold drawing
GD'11 Proceedings of the 19th international conference on Graph Drawing
Tight bound for farthest-color voronoi diagrams of line segments
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Visually exploring movement data via similarity-based analysis
Journal of Intelligent Information Systems
Normal art galleries: Wall in - all in
Computational Geometry: Theory and Applications
Fast vertex guarding for polygons with and without holes
Computational Geometry: Theory and Applications
Convex hull of points lying on lines in o(nlogn) time after preprocessing
Computational Geometry: Theory and Applications
Algorithms for fundamental spatial aggregate operations over regions
Proceedings of the 2nd ACM SIGSPATIAL International Workshop on Analytics for Big Geospatial Data
Hi-index | 0.01 |
The main contribution of this work is an O(n log n + k)-time algorithm for computing all k intersections among n line segments in the plane. This time complexity is easily shown to be optimal. Within the same asymptotic cost, our algorithm can also construct the subdivision of the plane defined by the segments and compute which segment (if any) lies right above (or below) each intersection and each endpoint. The algorithm has been implemented and performs very well. The storage requirement is on the order of n + k in the worst case, but it is considerably lower in practice. To analyze the complexity of the algorithm, an amortization argument based on a new combinatorial theorem on line arrangements is used.