The Cost of Complex Communication on Simple Networks

Endowing a communication network with the ability to realize arbitrary communication patterns is an expensive proposition, both in hardware and in system software. One might instead ask whether, for a given application program, a simple network can be built that performs well for that particular program. In this paper, we model an application program by the set of communication patterns it uses. We then consider the problem of determining when such a set of communication patterns is suitable for fast realization on a simple network. We show that the question of whether there exists a simple, inexpensive network for an algorithm is closely related to the VLSI layout question. In particular, we show how the VLSI framework can be used to produce a simple test that tells how complex such a network must be. Within this context we show that, contrary to common wisdom, the communication necessary for block-matrix transpose does not require complex hardware --- in fact, it is efficiently reali..