Deterministic Broadcasting Time with Partial Knowledge of the Network

We consider the time of deterministic broadcasting in networks whose nodes have limited knowledge of network topology. Each node v knows only the part of the network within knowledge radius r from it, i.e., it knows the graph induced by all nodes at distance at most r from v. Apart from that, each node knows the maximum degree of the network. One node of the network, called the source, has a message which has to reach all other nodes. We adopt the widely studied communication model called the one-way model in which, in every round, each node can communicate with at most one neighbor, and in each pair of nodes communicating in a given round, one can only send a message while the other can only receive it. This is the weakest of all store-and-forward models for point-to-point networks, and hence our algorithms work for other models as well, in at most the same time. We show trade-o7s between knowledge radius and time of deterministic broadcasting, when the knowledge radius is small, i.e., when nodes are only aware of their close vicinity. While for knowledge radius 0, minimum broadcasting time is 8(e), where e is the number of edges in the network, broadcasting can be usually completed faster for positive knowledge radius. Our main results concern knowledge radius 1. We develop fast broadcasting algorithms and analyze their execution time. We also prove lower bounds on broadcasting time, showing that our algorithms are close to optimal. c © 2002 Elsevier Science B.V. All rights reserved. A preliminary version of this paper will appear in Proceedings of the 11th Annual International Symposium on Algorithms and Computation (ISAAC’00), December 2000, Taipei, Taiwan. ∗ Corresponding author. E-mail addresses: [email protected] (G. De Marco), [email protected] (A. Pelc). 1 This research was done during the stay of Gianluca De Marco at the Universit@ e du Qu@ ebec B a Hull. 2 Supported in part by NSERC Grant OGP 0008136. 0304-3975/02/$ see front matter c © 2002 Elsevier Science B.V. All rights reserved. PII: S0304 -3975(02)00073 -7 2010 G. De Marco, A. Pelc / Theoretical Computer Science 290 (2003) 2009–2020