Gossiping and broadcasting versus computing functions in networks

The fundamental assumption in the classical theory of gossiping, broadcasting, and accumulation in networks is that atomic pieces of information are communicated in messages that consist of a set of such pieces. The communication mode in synchronous multiprocessor networks that are to compute a function does not fit this model. We show that, under certain assumptions about the way processors may communicate ("predictable reception"), computing an arbitrary n-ary function that has a "critical input" and distributing the result to all processors on an n-processor network takes at least as long as performing gossiping in the network graph. A similar relation exists between computing functions with the output appearing at only one processor and the complexity of broadcasting. Our methods can also be applied to extend known lower bounds for broadcasting a bit on EREW PRAMs to the much more general (randomized) distributed memory machines (DMMs).