Load-balancing iterative computations on heterogeneous clusters with shared communication links

We focus on mapping iterative algorithms onto heterogeneous clusters. The application data is partitioned over the processors, which are arranged along a virtual ring. At each iteration, independent calculations are carried out in parallel, and some communications take place between consecutive processors in the ring. The question is to determine how to slice the application data into chunks, and assign these chunks to the processors, so that the total execution time is minimized. A major difficulty is to embed a processor ring into a network that typically is not fully connected, so that some communication links have to be shared by several processor pairs. We establish a complexity result assessing the difficulty of this problem, and we design a practical heuristic that provides efficient mapping, routing, and data distribution schemes.