Data migration to minimize the total completion time

We consider the data migration problem, which is the problem of finding an efficient schedule to migrate data in a network. The data layout of a large storage server needs to be computed based on the expected data access pattern for load balancing. As the data access pattern changes over time, we need to recompute a new layout and then migrate the data from its current layout to the new layout. Our objective is to minimize the total completion time over all storage devices. We develop a 3-approximation algorithm when each migration job needs the same amount of time and a 9-approximation when the times required for different migration jobs are different. Another interesting objective is to minimize the total completion time over all data migration jobs. We present a 10-approximation algorithm when each migration job has a different processing time. We extend our results to the resource constrained scheduling problem where each job requires at most m resources. We obtain O(m)-approximations for both resource and job completion times.