Theoretical Computer Science
Optimal Non-preemptive Semi-online Scheduling on Two Related Machines
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Semi-online scheduling on two uniform processors
Theoretical Computer Science
Two semi-online scheduling problems on two uniform machines
Theoretical Computer Science
Geometric representation for semi on-line scheduling on uniform processors
Optimization Methods & Software - The 2nd Veszprem Optimization Conference: Advanced Algorithms (VOCAL), 13-15 December 2006, Veszprem, Hungary
Semi on-line algorithms for the partition problem
Operations Research Letters
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We consider semi on-line scheduling on two uniform machines. The speed of the slow machine is normalized to 1 while the speed of the fast machine is assumed to be s驴1. Jobs of size J 1,J 2,驴 arrive one at a time, and each J i (i驴1) has to be assigned to one of the machines before J i+1 arrives. The assignment cannot be changed later. The processing time of the ith job is J i on the slow machine and J i /s on the fast one. The objective is to minimize the makespan. We study both the case where the only information known in advance is the total size 驴 i驴1 J i of the jobs and the case where the only information known in advance is the optimum makespan. For each of these two cases, we almost completely determine the best possible competitive ratio of semi on-line algorithms compared to the off-line optimum, as a function of s in the range $1\le s , except for a very short subinterval around s=1.08. We also prove that the best competitive ratio achievable for known optimum is at least as good as the one for known sum, even for any number of uniform machines of any speeds.