Gossiping and Broadcasting versus Computing Functions in Networks

In the theory of dissemination of information in interconnection networks (gossiping and broadcasting) one assumes that a message consists of a set of distinguishable, atomic pieces of information, and that one communication pattern is used for solving a task. In this paper, a close connection is established between this theory and a situation in which functions are computed in synchronous networks without restrictions on the type of message used and with possibly di/erent communication patterns for di/erent inputs. The following restriction on the way processors communicate turns out to be essential: (∗) “Predictable reception”: At the beginning of a step a processor knows whether it is to receive a message across one of its links or not. We show that if (∗) holds then computing an n-ary function with a “critical input” (e.g., the OR of n bits) and distributing the result to all processors on an n-processor network G takes exactly as long as performing gossiping in G. Further we study the complexity of broadcasting one bit in a synchronous network, assuming that in one step a processor can send only one message, but without assuming (∗), and broadcasting one bit on parallel random-access machines (PRAMs) and distributed memory machines (DMMs) with the ARBITRARY access resolution rule. ? 2003 Elsevier B.V. All rights reserved.