Interprocessor communication with memory constraints

Many parallel applications require periodic redistribution of workloads and associated data. In a distributed memory computer, this redistribution can be difficult if limited memory is available for receiving messages. The authors propose a model for optimizing the exchange of messages under such circumstances which they call the minimum phase remapping problem. They first show that the problem is NP-Complete, and then analyze several methodologies for addressing it. First, they show how the problem can be phrased as an instance of multi-commodity flow. Next, they study a continuous approximation to the problem. They show that this continuous approximation has a solution which requires at most two more phases than the optimal discrete solution, but the question of how to consistently obtain a good discrete solution from the continuous problem remains open. Finally, they devise a simple and practical approximation algorithm for the problem with a bound of 1.5 times the optimal number of phases