Data Redistribution Algorithms for Homogeneous and Heterogeneous Processor Rings

We consider the problem of redistributing data on homogeneous and heterogeneous processor rings. The problem arises in several applications, each time after a load-balancing mechanism is invoked (but we do not discuss the load-balancing mechanism itself). We provide algorithms that aim at optimizing the data redistribution, both for unidirectional and bi-directional rings. One major contribution of the paper is that we are able to prove the optimality of the proposed algorithms in all cases except that of a bi-directional heterogeneous ring, for which the problem remains open.