A tradeoff between information and communication in broadcast protocols

Abstract

This paper concerns the message complexity of broadcast in arbitrary point-to-point communication networks. Broadcast is a task initiated by a single processor that wishes to convey a message to all processors in the network. We assume the widely accepted model of communication networks, in which each processor initially knows the identity of its neighbors, but does not know the entire network topology. Although it seems obvious that the number of messages required for broadcast in this model equals the number of links, no proof of this basic fact has been given before.

We show that the message complexity of broadcast depends on the exact complexity measure. If messages of unbounded length are counted at unit cost, then broadcast requires Θ(|V|) messages, where V is the set of processors in the network. We prove that if one counts messages of bounded length then broadcast requires Θ(|E|) messages, where E is the set of edges in the network.

Assuming an intermediate model in which each node knows the topology of the network in radius ρ ≥ 0 from itself, we prove tight upper and lower bounds of Θ(min{|E|, |V|^1+Θ(1)/ρ}) on the number of messages of bounded length required for broadcast. Both the upper and the lower bounds hold for both synchronous and asynchronous network models.

The same results hold for the construction of spanning trees, and various other global tasks.

Partially supported by Air Force contract TNDGAFOSR-86-0078, ARO contract DAAL03-86-K-0171 and NSF contract CCR8611442.

Partially supported by the New York Metropolitan Research Fund.

Partially supported by ONR contract N00014-85-C-0731.