Effective load balancing on highly parallel multicomputers based on superconcentrators

Tree and mesh architectures have been considered as two of the most highly scalable parallel multicomputers due to their scalabilities which are superior to those of hypercubes. However, the load balancing on these two multicomputer systems are not as well as we expected. The worst case of tree architecture requires O(M×p×logp) routing time for redistributing the workload over the system and it requires O(M×√p) for mesh architecture while pipelined packet routing scheme is used. In this paper, we propose an approach based on superconcentrators to reduce the above bounds to O(Mlogp) for both cases with only additional O(p) cost. Furthermore, by using this scheme, the underlying systems can leave the load balancing problem entirely to the superconcentrator so that there does not arise any additional workload of the systems. In addition, this scheme also adds extra communicating paths to the processors so that it not only increases the communication capacity among the processors but also could tolerate edge faults of the systems