  We study the expected completion time of some recently proposed algorithms
for distributed computing which redundantly assign computing tasks to multiple
machines in order to tolerate a certain number of machine failures. We
analytically show that not only the amount of redundancy but also the
task-to-machine assignments affect the latency in a distributed system. We
study systems with a fixed number of computing tasks that are split in possibly
overlapping batches, and independent exponentially distributed machine service
times. We show that, for such systems, the uniform replication of non-
overlapping (disjoint) batches of computing tasks achieves the minimum expected
computing time.
