An NC algorithm for finding a maximal acyclic set in a graph
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Many random walks are faster than one
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
How Well Do Random Walks Parallelize?
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
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We present fast and efficient parallel algorithms for finding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM. On a graph with n vertices and m edges, our randomized algorithm runs in O(log n) time using $(m+n^{1+\epsilon})/\log n$ EREW processors (for any fixed $\epsilon0$). A variant uses (m+n)/log n processors and runs in O(log n log log n) time. A deterministic version of the algorithm runs in $O(\log^{1.5}n)$ time using m+n EREW processors.