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
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
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
A new parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Constructing a maximal independent set in parallel
SIAM Journal on Discrete Mathematics
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
Simulating (logcn)-wise independence in NC
Journal of the ACM (JACM)
Information Processing Letters
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
Parallel search for maximal independence given minimal dependence
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On randomization in sequential and distributed algorithms
ACM Computing Surveys (CSUR)
Improved algorithms via approximations of probability distributions (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The algorithmic aspects of uncrowded hypergraphs
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Finding large independent sets of hypergraphs in parallel
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
A fast localized algorithm for scheduling sensors
Journal of Parallel and Distributed Computing - Special issue: Algorithms for wireless and ad-hoc networks
A global parallel algorithm for the hypergraph transversal problem
Information Processing Letters
Theoretical Computer Science
A new algorithm for the hypergraph transversal problem
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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A maximal independent set in a hypergraph is a subset of vertices that is maximal with respect to the property of not containing any edge of the hypergraph. We show that an algorithm proposed by Beame and Luby is in randomized NC for hypergraphs in which the maximum edge size is bounded by a constant. To prove this, we bound the upper tail of sums of dependent random variables defined on the edges of a hypergraph. These bounds may be viewed as extensions of bounds on the tail of the binomial distribution. We derandomize this algorithm to obtain the first sublinear time deterministic algorithm for hypergraphs with edges of size O(1). The algorithm exhibits the following time-processor tradeoff: it can be made to run in time O(n&egr;) with nO(1/&egr;) processors for a hypergraph on n vertices, for any &egr; ≥ 2d+1• (log log n)/(log n); here d = O(1) denotes the maximum size of an edge in H. In particular, for any constant &egr; O, we have an algorithm running in time O(n&egr;) on a polynomial number of processors, and we have an algorithm running in time (log n)O(1) on nO(log n/log log n) processors.