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
A new parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Improved lower bounds on k-independence
Journal of Graph Theory
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
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
Information Processing Letters
An efficient parallel algorithm that finds independent sets of guaranteed size
SIAM Journal on Discrete Mathematics
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Randomized algorithms
(De)randomized construction of small samples spaces in NC
Journal of Computer and System Sciences
Min-wise independent permutations (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A small approximately min-wise independent family of hash functions
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Parallel search for maximal independence given minimal dependence
SODA '90 Proceedings of the first 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
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A basic problem in hypergraphs is that of finding a large independent set-one of guaranteed size-in a given hypergraph. Understanding the parallel complexity of this and related independent set problems on hypergraphs is a fundamental open issue in parallel computation. Caro and Tuza (J. Graph Theory, Vol. 15, pp. 99-107, 1991) have shown a certain lower bound &agr;k(H) on the size of a maximum independent set in a given k-uniform hypergraph H, and have also presented an efficien sequential algorithm to find an independent set of size &agr;k (H). They also show that &agr;k (H) is the size of the maximum independent set for various hypergraph families. Here, we develop the first RNC algorithm to find an independent set of size &agr;k(H), and also derandomize it for various special cases. We also present lower bounds on independent set size and corresponding RNC algorithms for non-uniform hypergraphs.