Partition and task migration on k-extra-stage omega networks

In a large-scale parallel computing system the interconnection network is its key component. Partitionability of such a network is an important feature which allow multiple tasks to be run independently on different subsystems. Partitionable networks also provide fault-tolerant ability by localizing and disabling the minimal faulty subsystem so the entire system can gracefully sustain the normal computation. A task run on a subsystem may need to be migrated to another subsystem if the subsystem is faulty, or load balance is needed, or subsystem restructuring desired. Siegel et al. (1990) discussed the migration problem for Omega-equivalent networks. This paper studies the partitionability and presents an optimal task migration algorithm for k-extra-stage Omega networks