A SYNTHESIS OF AN OPTIMAL FILE TRANSFER ON A FILE TRANSMISSION NET

A file transmission net N is a directed communication net with vertex set V and arc set B such that each arc e has positive cost c(a)(e) and each vertex u in V has two parameters of positive cost c(v)(u) and nonnegative integral demand d(u). Some information to be distributed through N is supposed to have been written in a file and the written file is denoted by J, where the file means an abstract concept of information carrier. In this paper, we define concepts of file transfer, positive demand vertex set U and mother vertex set M, and we consider a problem of distributing d(v) copies of J through a file transfer on N from a vertex v1 to every vertex v in V. As a result, for N such that M subset-or-equal-to U, we propose an 0 (nm + n2 log n) algorithm, where n = Absolute value of V and m = Absolute value of B, for synthesizing a file transfer whose total cost of transmitting and making copies of J is minimum on N.