Optimal Non-preemptive Semi-online Scheduling on Two Related Machines

Abstract

We consider the following non-preemptive semi-online scheduling problem. Jobs with non-increasing sizes arrive one by one to be scheduled on two uniformly related machines, with the goal of minimizing the makespan. We analyze both the optimal overall competitive ratio, and the optimal competitive ratio as a function of the speed ratio (q ≥ 1) between the two machines. We show that the greedy algorithm LPT has optimal competitive ratio 1/4(1 + √17) ≈ 1.28 overall, but does not have optimal competitive ratio for every value of q. We determine the intervals of q where LPT is an algorithm of optimal competitive ratio, and design different algorithms of optimal competitive ratio for the intervals where it fails to be the best algorithm. As a result, we give a tight analysis of the competitive ratio for every speed ratio.KeywordsInput SequenceCompetitive RatioSpeed RatioIdentical MachineOnline ScheduleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.