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Practical Parallel Algorithms for Minimum Spanning Trees
 In Workshop on Advances in Parallel and Distributed Systems
, 1998
"... We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns ..."
Abstract

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We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns are efficient, both in theory and in practice. The algorithms are evaluated theoretically using Valiant's BSP model of parallel computation and empirically through implementation results.
5. Using Finite Experiments to Study Asymptotic Performance
"... In the analysis of algorithms we are interested in obtaining closed form expressions for algorithmic complexity, or at least asymptotic expressions in O(·)notation. It is often possible to use experimental results to make significant progress towards this goal, although there are fundamental reason ..."
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In the analysis of algorithms we are interested in obtaining closed form expressions for algorithmic complexity, or at least asymptotic expressions in O(·)notation. It is often possible to use experimental results to make significant progress towards this goal, although there are fundamental reasons whywe cannot guarantee to obtain such expressions from experiments alone. This paper investigates two approaches relating to problems of developing theoretical analyses based on experimental data. We first consider the scientific method, which views experimentation as part of a cycle alternating with theoretical analysis. This approach has been verysuccessful in the natural sciences. Besides supplying preliminary ideas for theoretical analysis, experiments can test falsifiable hypotheses obtained by incomplete theoretical analysis. Asymptotic behavior can also sometimes be deduced from stronger hypotheses which have been induced from experiments. As long as complete mathematical analyses remains elusive, well tested hypotheses may have to take their place. Several examples