including the one proposed in [5]. Minieka showed that all the eight problems can be solved in polynomial time except the one of finding the maximum distancesum tree of a specified length, which was proved to be NP-hard later in [8]. Recently, in [6,7], Peng and Lo have proposed efficient parallel algorithms on the EREW PRAM for optimally locating in a tree network a path and a tree of a specified length. They considered all the eight problems studied in Minieka's paper. In [6,7], it was assumed that the tree network is unweighted. Peng and Lo's results are