On the performance of on-line algorithms for partition problems
Acta Cybernetica
Online computation and competitive analysis
Online computation and competitive analysis
On-line scheduling of parallel jobs with runtime restrictions
Theoretical Computer Science
On an on-line scheduling problem for parallel jobs
Information Processing Letters
Parallel job scheduling — a status report
JSSPP'04 Proceedings of the 10th international conference on Job Scheduling Strategies for Parallel Processing
Online scheduling of parallel jobs on two machines is 2-competitive
Operations Research Letters
On-line scheduling of multi-core processor tasks with virtualization
Operations Research Letters
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We study the problem of on-line scheduling of parallel jobs on two machines. The jobs are parallel in the sense that each of them specifies the number of processors, in this case 1 or 2, required for simultaneous processing. The jobs are presented one by one. Upon receiving a job, we must assign the job to a time slot in the schedule before the next job is presented. No re-assignment is allowed. The goal is to minimize the makespan of the final schedule. There is a straightforward algorithm which achieves a competitive ratio of 2. In this paper we show that no on-line algorithm can have a competitive ratio less than 1+2/3(~1.816). We also study two special cases of the problem: (i) Jobs arrive in a non-decreasing order of processing times where we give an optimal algorithm with competitive ratio 3/2; (ii) Jobs arrive in a non-increasing order of processing times where we show that no on-line algorithm has a competitive ratio less than 9/7 and give a greedy algorithm with a competitive ratio 4/3.