Fast information sharing in a complete network

• Published in: Discrete Applied Mathematics Vol. 42; no. 1; pp. 75 - 86
• Main Authors: Sunderam, V.S., Winkler, Peter
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 26.02.1993; Amsterdam Elsevier; New York, NY
• Subjects: Applied sciences; Distributed computer systems; Electronics; Exact sciences and technology; Hardware; Processor; Distributed system; Interconnection; Sharing; Transmission protocol
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/0166-218X(93)90180-V

We consider the problem of complete information dissemination among n autonomous processors in a fully connected distributed system. Initially, each processor possesses information not held by any other processor; it is required that all the processors obtain all the information in the shortest possible time. Messages are exchanged in discrete, synchronized rounds; message size is unlimited, but during a round, each processor may transmit messages to, or receive messages from, at most k other processors. We show that ⌈log λ( k) n⌉ rounds are necessary for such an information exchange and that ⌈log λ( k) n⌉+3 are sufficient, where λ(k)= (k+ k 2+4 ) 2 . This settles in the affirmative a 10-year-old conjecture of Entringer and Slater; our lower bound is new even for the case k = 1.