On an Optimum File Transfer on a File Transmission Net

Yoshihiro KANEKO  Jiguang ZHANG  Shoji SHINODA  Kazuo HORIUCHI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.7   pp.1133-1138
Publication Date: 1993/07/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section of Letters Selected from the 1993 IEICE Spring Conference)
Category: 
Keyword: 
file transmission net,  file transfer,  optimal file transfer,  optimum file transfer,  

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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 MU holds.