A linear time algorithm for finding an optimal degree-bounded subtree of an edge-weighted tree

Given an edge-weighted tree T=(V(T),E(T)) and its subtree T^', for any v@?V(T), the distance d(v,T^') is defined as the minimum weighted distance from v to any vertex in T^'. The distance d(T,T^') is defined as the sum of all distances of the form d(v,T^') where v@?V(T). We give an algorithm to find a T^' that minimizes d(T,T^') and for all w@?V(T^'), the degree deg"T"^"'(w) of w is not more than a prespecified bound db(w)(0=