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On an Optimum File Transfer on a File Transmission Net
Yoshihiro KANEKO Jiguang ZHANG Shoji SHINODA Kazuo HORIUCHI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1993/07/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section of Letters Selected from the 1993 IEICE Spring Conference)
file transmission net, file transfer, optimal file transfer, optimum file transfer,
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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.