Abstract
Gossiping is the process of information diffusion in which each node of a network holds a packet that must be communicated to all other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a fixed number p of packets at each round. In the first part of the paper we study the extremal case p = 1 and we exactly determine the optimal number of communication rounds to perform gossiping for several classes of graphs, including Hamiltonian graphs and complete k-ary trees. For arbitrary graphs we give asymptotically matching upper and lower bounds. We also study the case of arbitrary p and we exactly determine the optimal number of communication rounds to perform gossiping under this hypothesis for complete graphs, hypercubes, rings, and paths.
The work of the first author was partially supported by the French GDR/PRC Project PRS. He wants also to thank the Dipartimento di Informatica ed Applicazioni of the Università di Salerno, where part of his research was done, for inviting him. The work of the last three authors was partially supported by Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo of C.N.R. under Grant No. 92.01622.PF69 and by the Italian Ministry of the University and Scientific Research, Project: Algoritmi, Modelli di Calcolo e Strutture Informative.
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Bermond, J.C., Gargano, L., Rescigno, A.A., Vaccaro, U. (1995). Fast gossiping by short messages. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_69
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DOI: https://doi.org/10.1007/3-540-60084-1_69
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