Bounding Distributions for the Weight of a Minimum Spanning Tree in Stochastic Networks

Authors:
Kevin R. Hutson;Douglas R. Shier
Affiliations:
Department of Mathematics and Computer Science, Denison University, Granville, Ohio 43023;Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634
Venue:
Operations Research
Year:
2005

Citing 2
Cited 2

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Discrete Applied Mathematics
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Learning automata-based algorithms for solving stochastic minimum spanning tree problem

Applied Soft Computing
A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs

The Journal of Supercomputing

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Abstract

This paper considers the problem of determining the distribution of the weight W of a minimum spanning tree for an undirected graph with edge weights that are independently distributed discrete random variables. Using the underlying fundamental cutsets and cycles associated with a spanning tree, we are able to obtain upper and lower bounds on the distribution of W. In turn, these are used to establish bounds on E[W]. Our general method for deriving these bounding distributions subsumes existing approximation methods in the literature. Computational results indicate that the new approximation methods provide excellent bounds for some challenging test networks.