Parallel scheduling algorithm to minimize maximal cost

Considers a scheduling problem, where n jobs are to be processed on a single machine, precedence constraints among the jobs are given and preemption is allowed. For each job i, there is known a release date r _i representing the earliest possible starting time of the job and a processing time p_i. Moreover, precedence constraints are given among the jobs. The precedence constraints are described by a digraph. The problem considered is polynomially solvable. In this paper, a parallel algorithm is proposed, which allows one to solve the problem in polylogarithmic time using polynomial number of parallel processors