On an Optimum File Transfer on a File Transmission Net

Yoshihiro KANEKO, Jiguang ZHANG, Shoji SHINODA, Kazuo HORIUCHI

Summary :

In a file transmission net N with vertex set V and arc set B, copies of a file J are distributed from a vertex to every vertex, subject to certain rules on file transmission. A cost of making one copy of J at each vertex µ is called a copying cost at µ, a cost of transmitting one copy of J through each arc (x, y) is called a transmission cost (x, y), and the number of copies of J demanded at each vertex u in N is called a copy demand at u. A scheduling of distributing copies of J from a vertex, say s, to every vertex on N is called a file transfer from s. The vertex s is called the source of the file transfer. A cost of a file transfer is defined, a file transfer from s is said to be optimal if its cost is not larger than the cost of any other file transfer from s, and an optimal file transfer from s is said to be optimum on N if its cost is not larger than that of an optimal file transfer from any other vertex. In this note, it is proved that an optimal file transfer from a vertex with a minimum copying cost is optimum on N, if there holds M U where M and U are the mother vertex set and the positive demand vertex set of N, respectively. Also it is shown by using an example that an optimal file transfer from a vertex with a minimum copying cost is not always optimum on N when M ⊃ U holds.

• Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.7 pp.1133-1138
• Publication Date: 1993/07/25
• Type of Manuscript: Special Section LETTER (Special Section of Letters Selected from the 1993 IEICE Spring Conference)

Authors

Yoshihiro KANEKO
Jiguang ZHANG
Shoji SHINODA
Kazuo HORIUCHI

Keyword

file transmission net,  file transfer,  optimal file transfer,  optimum file transfer