On the Optimality of Forest-Type File Transfers on a File Transmission Net

A problem of obtaining an optimal file transfer on a file transmission net N is to consider how to transmit, with a minimum total cost, copies of a certain file of information from some vertices to others on N by the respective vertices’ copy demand numbers. This problem is NP-hard for a general file transmission net. So far, some class of N on which polynomial time algorithms for obtaining an optimal file transfer are designed has been known. In addition, if we deal with restricted file transfers, i.e., forest-type file transfers, we can obtain an optimal ‘foresttype’ file transfer on more general class of N . This paper proves that for such general nets it suffices to consider forest-type file transfers in order to obtain an optimal file transfer. key words: le transfer, optimality, minimum cost, forest-type