Computing capacitated minimal spanning trees efficiently

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Abstract
An analysis is made of the computational complexity of a class of heuristic algorithms for the solution of the minimal spanning tree problem subject to a restriction on the maximum number (or weight) of nodes in any subtree rooted at a distinguished node. This is of particular interest in designing networks with branch capacity restrictions. The algorithm is a modification of Kruskal's Algorithm where weights are assigned to the nodes and then used, along with the arc lengths, to select the order in which arcs are considered for inclusion in the spanning tree. Considerations in the efficient implementation of such algorithms are examined and several heuristics for assigning node weights are compared.

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