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

Two models for message passing parallel systems 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. The goal of the article 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: techniques for measurement of the value of λ on a given machine; creating efficient broadcast algorithms that get the latency λ and the number of nodes n as parameters; and 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 Intel Delta machine. The 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%