A polynomial algorithm for some preemptive multiprocessor task scheduling problems

In this paper we consider a problem of preemptive scheduling of multiprocessor tasks on dedicated processors in order to minimize the sum of completion times. Using a standard notation, our problem can be denoted as P ∣ fixj, pmtn ∣ ∑Cj. We give a polynomial-time algorithm to solve P ∣ fixj, G = {P4, dart}-free, pmtn ∣ ∑Cj problem. This result generalizes the following problems: P2 ∣ fixj, pmtn ∣ ∑Cj, P ∣ ∣fixj∣ ∈ {1, m}, pmtn ∣ ∑Cj and P4 ∣ fixj = 2, pmtn ∣ ∑Cj.