A fast parallel algorithm for the maximal independent set problem
Journal of the ACM (JACM)
A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
A randomized algorithm for closest-point queries
SIAM Journal on Computing
Polling: a new randomized sampling technique for computational geometry
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Compact distributed data structures for adaptive routing
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The complexity of many faces in arrangements of lines of segments
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
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Partitioning arrangements of lines, part I: an efficient deterministic algorithm
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Parallel algorithms for arrangements
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
Constructing arrangements optimally in parallel (preliminary version)
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Information and Computation
A deterministic view of random sampling and its use in geometry
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Removing randomness in parallel computation without a processor penalty
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
The probabilistic method yields deterministic parallel algorithms
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Geometric partitioning made easier, even in parallel
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
A parallel approximation algorithm for positive linear programming
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Almost optimal set covers in finite VC-dimension: (preliminary version)
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
Improved algorithms via approximations of probability distributions (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Noise-tolerant parallel learning of geometric concepts
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Noise-tolerant distribution-free learning of general geometric concepts
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Incremental Reconfiguration and Load Adjustment in Adaptive Real-Time Systems
IEEE Transactions on Computers
Noise-tolerant distribution-free learning of general geometric concepts
Journal of the ACM (JACM)
On linear-time deterministic algorithms for optimization problems in fixed dimension
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Fixed-dimensional parallel linear programming via relative &egr;-approximations
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
New approaches to covering and packing problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science - Algorithmic learning theory
Topology control and routing in ad hoc networks: a survey
ACM SIGACT News
An efficient distributed algorithm for constructing small dominating sets
Distributed Computing - Special issue: Selected papers from PODC '01
Constant-time distributed dominating set approximation
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Finding r-Dominating Sets and p-Centers of Trees in Parallel
IEEE Transactions on Parallel and Distributed Systems
Constant-time distributed dominating set approximation
Distributed Computing
Proceedings of the 19th international conference on World wide web
Set cover algorithms for very large datasets
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
Linear-work greedy parallel approximate set cover and variants
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Densest subgraph in streaming and MapReduce
Proceedings of the VLDB Endowment
Parallel and I/O efficient set covering algorithms
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Parallel data mining revisited. better, not faster
IDA'12 Proceedings of the 11th international conference on Advances in Intelligent Data Analysis
Fast greedy algorithms in mapreduce and streaming
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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In this paper we give the first NC approximation algorithms for the unweighted and weighted set cover problems. Our algorithms use a linear number of processors and give a cover that has at most log n times the optimal size/weight, thus matching the performance of the best sequential algorithms. We apply our set cover algorithm to learning theory, giving an NC algorithm to learn the concept class obtained by taking the closure under finite union or finite intersection of any concept class of finite VC-dimension that has an NC hypothesis finder. In addition, we give a linear-processor NC algorithm for a variant of the set cover problem first proposed by Chazelle and Friedman and use it to obtain NC algorithms for several problems in computational geometry.