Preemptive scheduling of independent jobs on identical parallel machines subject to migration delays

We present, hardness and approximation results for the problem of scheduling n independent jobs on m, identical parallel machines subject to a migration delay d so as to minimize the makespan. We give a sharp threshold on the value of d for which the complexity of the problem changes from polynomial time solvable to NP-hard. We give initial results supporting a conjecture that there always exists an optimal schedule in which at most m - 1 jobs migrate. Further, we give a O(n) time O(1+1/log(2) n)-approximation algorithm for m = 2, and show that there is a polynomial tirne approximation scheme for arbitrary m.