Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
On k-hulls and related problems
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
SIAM Journal on Computing
A randomized algorithm for closest-point queries
SIAM Journal on Computing
Parallel construction of subdivision hierarchies
Journal of Computer and System Sciences
An optimal-time algorithm for slope selection
SIAM Journal on Computing
An optimal parallel algorithm for building a data structure for planar point location
Journal of Parallel and Distributed Computing
A guided tour of Chernoff bounds
Information Processing Letters
Introduction to algorithms
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
Selecting distances in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Enumerating k distances for n points in the plane
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
Cutting hyperplane arrangements
Discrete & Computational Geometry
An optimal convex hull algorithm and new results on cuttings (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Discrepancy and &egr; approximations for bounded VC-dimension
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Optimal parallel randomized algorithms for three-dimensional convex hulls and related problems
SIAM Journal on Computing
An introduction to parallel algorithms
An introduction to parallel algorithms
Applications of parametric searching in geometric optimization
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Diameter, width, closest line pair, and parametric searching
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Efficient NC algorithms for set cover with applications to learning and geometry
Proceedings of the 30th IEEE symposium on Foundations of computer science
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
Derandomizing an output-sensitive convex hull algorithm in three dimensions
Computational Geometry: Theory and Applications
On linear-time deterministic algorithms for optimization problems in fixed dimension
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Chernoff-Hoeffding bounds for applications with limited independence
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Geometric Partitioning and Its Applications
Geometric Partitioning and Its Applications
Techniques for computing with low-independence randomness
Techniques for computing with low-independence randomness
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Almost optimal set covers in finite VC-dimension: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A parallel algorithm for linear programming in fixed dimension
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
On computing Voronoi diagrams by divide-prune-and-conquer
Proceedings of the twelfth annual symposium on Computational geometry
Proceedings of the twelfth annual symposium on Computational geometry
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Construction of 1-d lower envelopes and applications
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
On enumerating and selecting distances
Proceedings of the fourteenth annual symposium on Computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Fixed-dimensional parallel linear programming via relative &egr;-approximations
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Optimal point placement for mesh smoothing
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Methods for achieving fast query times in point location data structures
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Optimal, Output-Sensitive Algorithms for Constructing Upper Envelope of Line Segments in Parallel
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Improved Deterministic Parallel Padded Sorting
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Faster output-sensitive parallel algorithms for 3D convex hulls and vector maxima
Journal of Parallel and Distributed Computing
Dynamic algorithms for approximating interdistances
Nordic Journal of Computing
Dynamic algorithms for approximating interdistances
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A Deterministic Linear Time Algorithm For Geometric Separators And Its Applications
Fundamenta Informaticae
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We present a simple approach for constructing geometric partitions in a way that is easy to apply to new problems. We avoid the use of VC-dimension arguments, and, instead, base our arguments on a notion we call the scaffold dimension, which subsumes the VC-dimension and is simpler to apply. We show how to easily construct (1/r)-nets and (1/r)-approximations for range spaces with bounded scaffold dimension, which immediately implies simple algorithms for constructing (1/r)-cuttings (by straight-forward recursive subdivision methods). More significant than simply being a conceptual simplification of previous approaches, however, is that our methods lead to asymptotically faster and more-efficient EREW PRAM parallel algorithms for a number of computational geometry problems, including the development of the first optimal-work NC algorithm for the well-known 3-dimensional convex hull problem, which solves an open problem of Amato and Preparata. Interestingly, our approach also yields a faster sequential algorithm for the distance selection problem, by the parametric searching paradigm, which solves an open problem posed by Agarwal, Aronov, Sharir, and Suri, and reiterated by Dickerson and Drysdale.