A fast parallel algorithm for the maximal independent set problem
Journal of the ACM (JACM)
A taxonomy of problems with fast parallel algorithms
Information and Control
Parallel algorithms for depth-first searches I. planar graphs
SIAM Journal on Computing
Constructing a perfect matching is in random NC
Combinatorica
A parallel algorithm for the maximal path problem
Combinatorica - Theory of Computing
Matching is as easy as matrix inversion
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Parallelism and greedy algorithms
Parallelism and greedy algorithms
The complexity of parallel computations
The complexity of parallel computations
Derandomization through approximation: an NC algorithm for minimum cuts
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
An efficient parallel algorithm that finds independent sets of guaranteed size
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A 2-approximation NC algorithm for connected vertex cover and tree cover
Information Processing Letters
A new parallel algorithm for the maximal independent set problem
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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In this paper we present a fast parallel algorithm for constructing a depth first search tree for an undirected graph. The algorithm is an RNC algorithm, meaning that it is a probabilistic algorithm that runs in polylog time using a polynomial number of processors on a P-RAM. The run time of the algorithm is &Ogr;(TMM(n)log3n), and the number of processors used is PMM(n) where TMM(n) and PMM(n) are the time and number of processors needed to find a minimum weight perfect matching on an n vertex graph with maximum edge weight n.