Online Scheduling with Unit Processing Times and Processing Set Restrictions

Abstract

This paper investigates online scheduling problems with processing set restrictions. There is a sequence of jobs that are revealed one by one over list, where each job has unit processing time. A job can only be processed by a subset of the machines, namely the processing set of the job. The objective is to minimize the makespan. For m machines with two different processing sets, we propose an optimal algorithm with a competitive ratio of $$\\frac{3}{2}$$\n . For three machines with inclusive processing sets, an optimal algorithm with competitive ratio $$\\frac{5}{3}$$\n is provided.