A Polynomially Solvable Case of Scheduling Multiprocessor Tasks in a Multi-Machine Environment

Abstract

Abstract. The problem of scheduling multiprocessor tasks in a multi-machine environment is considered. Each machine contains a number of identical processors. Each task requires a number of processors on a single machine for its processing. The objective is to minimize the overall task completion time, i.e. the makespan. The general problem has been known to be strongly NP-hard. A linear time optimal algorithm is presented for a special case of the problem where all the tasks have unit processing times and each task requires one or k (k is part of the input) processors. The small computational effort of the algorithm is valuable in some practical applications.