Interprocessor Communication with Limited Memory

Abstract—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. Index Terms—Interprocessor communication, dynamic load balancing, data migration, scheduling, NP-completeness, approximation algorithms.