Abstract
Assume that a graph G has l sources, each assigned a non-negative integer called a supply, that all the vertices other than the sources are sinks, each assigned a non-negative integer called a demand, and that each edge of G is assigned a non-negative integer, called a capacity. Then one wishes to find a spanning forest F of G such that F consists of l trees, each tree T in F contains a source w, and the flow through each edge of T does not exceed the edge-capacity when a flow of an amount equal to a demand is sent from w to each sink in T along the path in T. Such a forest F is called a spanning distribution forest of G. In the paper, we first present a pseudo-polynomial time algorithm to find a spanning distribution forest of a given series-parallel graph, and then extend the algorithm for graphs with bounded tree-width.
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Inoue, K., Nishizeki, T. (2014). Spanning Distribution Forests of Graphs. In: Chen, J., Hopcroft, J.E., Wang, J. (eds) Frontiers in Algorithmics. FAW 2014. Lecture Notes in Computer Science, vol 8497. Springer, Cham. https://doi.org/10.1007/978-3-319-08016-1_11
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DOI: https://doi.org/10.1007/978-3-319-08016-1_11
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