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 a perfect matching is in random NC
Combinatorica
Balancing vectors in the max norm
Combinatorica
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Efficient parallel algorithms for edge coloring problems
Journal of Algorithms
The complexity of parallel search
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Balanced two-colorings of finite sets in the cube
Discrete Mathematics - Proceedings of the Oberwolfach Meeting "Kombinatorik," January 19-25, 1986
A randomized algorithm for closest-point queries
SIAM Journal on Computing
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
Simulating (logcn)-wise independence in NC
Journal of the ACM (JACM)
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Optimal Randomized Parallel Algorithms for Computational Geometry I
Optimal Randomized Parallel Algorithms for Computational Geometry I
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
Efficient NC algorithms for set cover with applications to learning and geometry
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
A fast parallel algorithm for routing in permutation networks
IEEE Transactions on Computers
Deterministic sampling—a new technique for fast pattern matching
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Clique partitions, graph compression and speeding-up algorithms
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Simulating (logcn)-wise independence in NC
Journal of the ACM (JACM)
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Sample spaces uniform on neighborhoods
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On the parallel complexity of computing a maximal independent set in a hypergraph
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Fast randomized algorithms for distributed edge coloring
PODC '92 Proceedings of the eleventh annual ACM symposium on Principles of distributed computing
Geometric partitioning made easier, even in parallel
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
More deterministic simulation in logspace
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Constructing small sample spaces satisfying given constraints
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
On randomization in sequential and distributed algorithms
ACM Computing Surveys (CSUR)
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On construction of k-wise independent random variables
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
The amazing power of pairwise independence (abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Paul Erdös (1913-996): his influence on the theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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
An extension of the Lovász local lemma, and its applications to integer programming
Proceedings of the seventh 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
Nearly optimal distributed edge colouring in O(log log n) rounds
SODA '97 Proceedings of the eighth 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
Algorithmic derandomization via complexity theory
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximating Scheduling Unrelated Parallel Machines in Parallel
Computational Optimization and Applications
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Fast parallel edge colouring of graphs
Journal of Parallel and Distributed Computing - Special section best papers from the 2002 international parallel and distributed processing symposium
Finding a vector orthogonal to roughly half a collection of vectors
Journal of Complexity
Small Sample Spaces Cannot Fool Low Degree Polynomials
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Pseudorandom Bit Generators That Fool Modular Sums
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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We present a technique for converting RNC algorithms into NC algorithms. Our approach is based on a parallel implementation of the method of conditional probabilities. This method was used to convert probabilistic proofs of existence of combinatorial structures into polynomial time deterministic algorithms. It has the apparent drawback of being extremely sequential in nature. We show certain general conditions under which it is possible to use this technique for devising deterministic parallel algorithms. We use our technique to devise an NC algorithm for the set balancing problem. This problem turns out to be a useful tool for parallel algorithms. Using our de-randomization method and the set balancing algorithm, we provide an NC algorithm for the lattice approximation problem. We also use the lattice approximation problem to bootstrap the set balancing algorithm, and the result is a more processor efficient algorithm. The set balancing algorithm also yields an NC algorithm for near-optimal edge coloring of simple graphs. Our methods also extend to the parallelization of various algorithms in computational geometry that rely upon the random sampling technique of Clarkson. Finally, our methods apply to constructing certain combinatorial structures, e.g., Ramsey graphs and independent sets and covers of hypergraphs.