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 different communication patterns for different 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. (C) 2003 Elsevier B.V. All rights reserved.