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A new parallel algorithm for the maximal independent set problem (MIS) is constructed. It runs in O(log4 n) time when implemented on a linear number of EREW-processors. This is the first deterministic algorithm for MIS whose running time is polylogarithmic and whose processor-time product is optimal up to a polylogarithmic factor.
In practice, the average time of (deterministic or randomized) sorting algorithms seems to be more relevant than the worst case time of deterministic algorithms. Still, the many known complexity bounds for parallel comparison sorting include no nontrivial lower bounds for the average time required to sort by comparisons n elements with p processors (via deterministic or randomized algorithms). We...
This paper considers mesh computers with buses, where each bus provides a broadcasting capability to the processors connected to it. We first disprove a published claim by showing that on a 2-dimensional mesh with a bus for each row, where each row must solve its own problem with data that is independent of all other rows, there are problems where the rows can cooperatively solve all subproblems faster...
Universal networks offer the advantage that they can execute programs written for simpler architectures without significant run-time overhead. In this paper we investigate simulations of tree machines; the fact that divide-and-conquer algorithms are programmed naturally on trees motivates our investigation. Among various proposals for parallel computing the boolean hypercube has emerged as a particularly...
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...
The time complexity of sorting n elements using p ≥ n processors on Valiant's parallel comparison tree model is considered. The following results are obtained. 1. We show that this time complexity is Θ(logn/log(1+p/n)). This complements the AKS sorting network in settling the wider problem of comparison sort of n elements by p processors, where the problem for p ≤ n was resolved. To prove the lower...
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