Spanning distribution forests of graphs (extended abstract)

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. © 2014 Springer International Publishing.