On the design and implementation of broadcast and global combine operations using the postal model

There are a number of models that were proposed in recent years for message passing parallel systems. Examples are the postal model and its generalization the LogP model. In the postal model a parameter λ is used to model the communication latency of the message-passing system. Each node during each round can send a fixed-size message and, simultaneously, receive a message of the same size. Furthermore, a message sent out during round r will incur a latency of λ and will arrive at the receiving node at round r+λ-1. Our goal in this paper is to bridge the gap between the theoretical modeling and the practical implementation. In particular, we investigate a number of practical issues related to the design and implementation of two collective communication operations, namely, the broadcast operation and the global combine operation. Those practical issues include, for example, (1) techniques for measurement of the value of λ on a given machine, (2) creating efficient broadcast algorithms that get the latency h and the number of nodes n as parameters and (3) creating efficient global combine algorithms for parallel machines with λ which is not an integer. We propose solutions that address those practical issues and present results of an experimental study of the new algorithms on the Inter Delta machine. Our main conclusion is that the postal model can help in performance prediction and tuning, for example, a properly tuned broadcast improves the known implementation by more than 20%