  In this work we are interested in the problem of scheduling and
redistributing data on master-slave platforms. We consider the case were the
workers possess initial loads, some of which having to be redistributed in
order to balance their completion times. We examine two different scenarios.
The first model assumes that the data consists of independent and identical
tasks. We prove the NP-completeness in the strong sense for the general case,
and we present two optimal algorithms for special platform types. Furthermore
we propose three heuristics for the general case. Simulations consolidate the
theoretical results. The second data model is based on Divisible Load Theory.
This problem can be solved in polynomial time by a combination of linear
programming and simple analytical manipulations.
