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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. We propose a model for optimizing the exchange of messages under such circumstances which we call the minimum phase remapping problem. We first show that the problem is NP-complete, and then analyze several methodologies for addressing it. First, we show how the problem can be phrased as an instance of multicommodity flow. Next, we study a continuous approximation to the problem. We 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. We also devise a simple and practical approximation algorithm for the problem with a bound of 1.5 times the optimal number of phases. We also present an empirical study of variations of our algorithms which indicate that our approaches are quite practical.