The present disclosure relates to assignment or generation of reducer virtual machines after the “map” phase is substantially complete in MapReduce. Instead of a priori placement, distribution of keys after the “map” phase over the mapper virtual machines can be used to efficiently reducer tasks in virtualized cloud infrastructure like OpenStack. By solving a constraint optimization problem, reducer VMs can be optimally assigned to process keys subject to certain constraints. In particular, the present disclosure describes a special variable matrix. Furthermore, the present disclosure describes several possible cost matrices for representing the costs determined based on the key distribution over the mapper VMs (and other suitable factors).