Proceedings ArticleDOI
An optimal randomized parallel algorithm for finding connected components in a graph
Hillel Gazit
- pp 492-501
TLDR
This work presents a parallel randomized algorithm for finding the connected components of an undirected graph that is Optimal in space as well.Abstract:
We present a parallel randomized algorithm for finding the connected components of an undirected graph. Our algorithm takes T = O(log (n)) time and p = O(m+n/(log(n) processors, where m = number of edges and n = number of vertices. This algorithm improves the results of Cole and Vishkin1, which use O(log (n)?log (log (n))?log (log (log (n)))) time. Our algorithm is Optimal in the sense that the product P?T is a linear function of the input size. The algorithm requires O(m + n) space which is the input size, so it is Optimal in space as well.read more
Citations
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References
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A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
TL;DR: In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.
Journal ArticleDOI
An O(logn) parallel connectivity algorithm
Yossi Shiloach,Uzi Vishkin +1 more
TL;DR: It is conjectured that the barrier of O(log n) cannot be surpassed by any polynomial number of processors and that this performance cannot be achieved in the weaker model.
Book
An Efficient Parallel Biconnectivity Algorithm
Robert E. Tarjan,Uzi Vishkin +1 more
TL;DR: A new algorithm for finding the blocks (biconnected components) of an undirected graph and a general algorithmic technique that simplifies and improves computation of various functions on trees is introduced.
Proceedings ArticleDOI
Parallel tree contraction and its application
Gary L. Miller,John H. Reif +1 more
TL;DR: A bottom-up algorithm to handle trees which has two major advantages over the top-down approach: the control structure is straight forward and easier to implement facilitating new algorithms using fewer processors and less time; and problems for which it was too difficult or too complicated to find polylog parallel algorithms are now easy.
Proceedings ArticleDOI
Deterministic coin tossing and accelerating cascades: micro and macro techniques for designing parallel algorithms
Richard Cole,Uzi Vishkin +1 more
TL;DR: A new deterministic coin tossing technique that provides for a fast and eff ient b reak ing of a symmetr ic s i tuat ion in paral le l is introduced.