Distributed broadcast in radio networks of unknown topology

Authors:
Andrea E. F. Clementi;Angelo Monti;Riccardo Silvestri
Affiliations:
Dipartimento di Matematica, Università di Roma, Via della Ricerca Scientifica, "Tor Vergata", Rome I-00133, Italy;Dipartimento di Informatica, Università "La Sapienza" di Roma, Italy;Dipartimento di Informatica, Università "La Sapienza" di Roma, Italy
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

A multi-hop synchronous radio network is said to be unknown if the nodes have no knowledge of the topology. A basic task in radio network is that of broadcasting a message (created by a fixed source node) to all nodes of the network. Typical operations in real-life radio networks is the multi-broadcast that consists in performing a set of r independent broadcasts. The study of broadcast operations on unknown radio network is started by the seminal paper of Bar-Yehuda et al. [J. Comput. System Sci. 45 (1992) 104] and has been the subject of several recent works.In this paper, we study the completion and the termination time of distributed protocols for both the (single) broadcast and the multi-broadcast operations on unknown networks as functions of the number of nodes n, the maximum eccentricity D, the maximum in-degree Δ, and the congestion c of the networks. We establish new connections between these operations and some combinatorial concepts, such as selective families, strongly selective families (also known as superimposed codes), and pairwise r-different families. Such connections, combined with a set of new lower and upper bounds on the size of the above families, allow us to derive new lower bounds and new distributed protocols for the broadcast and multi-broadcast operations. In particular, our upper bounds are almost tight and strongly improve over the previous bounds for a large class of networks.