Multiway cut and integer flow problems in trees

Let T = ( V , E ) be a n-vertices undirected tree and X ⊂ V a set of terminal vertices. We consider the well-know multway cut problem to which we associate the problem of finding an integral multiway flow maximizing the flow routed between all pair of terminals. These problems are special cases of multicut and integral multiflow problems which are know to be NP-hard in tress. We propose a generic procedure to explore and reduce a tree, which allows to devise an O ( n ) procedure for the multiway cut and an O ( n 2 ) procwdure for the integral multiway flow in trees. Efficient procedured are also proposed to solve the problems in directed trees.