These algorithms were studied even before the right complexity measures and problems were isolated. The optimal solution T to MST . Edmonds, J. Optimum branchings . A reverse arborescence rooted at r is one with edges directed towards r, i.e. all nodes except r have outdegree one and r has outdegree zero. Optimum branchings .
Trees are more general than chains because each chain is a tree.
Optimum branching . Tamir studied several combinatorial optimization games which or its special cases can be reduced to the Owen s linear production game model. Let n and m denote the number of vertices and the number of arcs of D, respectively. A spanning branching is any branching that includes all nodes in the graph. These algorithms can be used to find the branching with the highest score regardless of the metric we use, as long as one can associate a weight with every edge.