Matrix multiplication on heterogeneous platforms

In this paper, we address the issue of implementing matrix multiplication o n heterogeneous platforms. We target two different classes of heterogeneous computing resources: heterogeneous networks of workstations and collection s of heterogeneous clusters. Intuitively, the problem is to load balance th e work with different speed resources while minimizing the communication vo lume. We formally state this problem in a geometric framework and prove its NP-completeness. Next, we introduce a (polynomial) column-based heuristic, which turns out to be very satisfactory: We derive a theoretical performan ce guarantee for the heuristic and we assess its practical usefulness throu gh MPI experiments.