The number of small semispaces of a finite set of points in the plane
Journal of Combinatorial Theory Series A
Halfspace range search: an algorithmic application of k-sets
Discrete & Computational Geometry
More on k-sets of finite sets in the plane
Discrete & Computational Geometry
The ultimate planar convex hull algorithm
SIAM Journal on Computing
A probabilistic algorithm for the post office problem
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Partitioning and geometric embedding of range spaces of finite Vapnik-Chervonenkis dimension
SCG '87 Proceedings of the third annual symposium on Computational geometry
An O (n log log n)-time algorithm for triangulating a simple polygon
SIAM Journal on Computing
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
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A geometric consistency theorem for a symbolic perturbation scheme
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
On k-hulls and related problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
ACM SIGACT News
Polling: a new randomized sampling technique for computational geometry
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
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
A deterministic algorithm for partitioning arrangements of lines and its application
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
A fast planar partition algorithm, II
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
An efficient algorithm for hidden surface removal
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Randomized algorithms for binary search and load balancing with geometric applications
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Cutting hyperplane arrangements
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Output sensitive construction of levels and Voronoi diagrams in Rd of order 1 to k
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A fast planar partition algorithm, I
Journal of Symbolic Computation
An algorithm for generalized point location and its applications
Journal of Symbolic Computation
A fast planar partition algorithm, II
Journal of the ACM (JACM)
Optimal sample cost residues for differential database batch query problems
Journal of the ACM (JACM)
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
ACM Computing Surveys (CSUR)
Accelerated occlusion culling using shadow frusta
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Constructing cuttings in theory and practice
Proceedings of the fourteenth annual symposium on Computational geometry
The Clarkson–Shor Technique Revisited and Extended
Combinatorics, Probability and Computing
On the set multi-cover problem in geometric settings
Proceedings of the twenty-fifth annual symposium on Computational geometry
Obstacle discovery in distributed actuator and sensor networks
ACM Transactions on Sensor Networks (TOSN)
Algorithms for dominating set in disk graphs: breaking the log n Barrier
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Scalable Uniform Graph Sampling by Local Computation
SIAM Journal on Scientific Computing
Geometric packing under non-uniform constraints
Proceedings of the twenty-eighth annual symposium on Computational geometry
On the set multicover problem in geometric settings
ACM Transactions on Algorithms (TALG)
Adaptive stratified reservoir sampling over heterogeneous data streams
Information Systems
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Random sampling is used for several new geometric algorithms. The algorithms are “Las Vegas,” and their expected bounds are with respect to the random behavior of the algorithms. One algorithm reports all the intersecting pairs of a set of line segments in the plane, and requires &Ogr;(A + n log n) expected time, where A is the size of the answer, the number of intersecting pairs reported. The algorithm requires &Ogr;(n) space in the worst case. Another algorithm computes the convex hull of a point set in E3 in &Ogr;(n log A) expected time, where n is the number of points and A is the number of points on the surface of the hull. A simple Las Vegas algorithm triangulates simple polygons in &Ogr;(n log log n) expected time. Algorithms for half-space range reporting are also given. In addition, this paper gives asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets.