Scheduling independent tasks on uniform processors
SIAM Journal on Computing
Tighter bounds for LPT scheduling on uniform processors
SIAM Journal on Computing
Semi-online scheduling with decreasing job sizes
Operations Research Letters
Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data
Information and Computation
Optimal preemptive semi-online scheduling on two uniform processors
Information Processing Letters
Semi-online scheduling jobs with tightly-grouped processing times on three identical machines
Discrete Applied Mathematics - Special issue: Max-algebra
Semi-online scheduling on two uniform processors
Theoretical Computer Science
Semi-online scheduling jobs with tightly-grouped processing times on three identical machines
Discrete Applied Mathematics
Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data
Information and Computation
Optimal preemptive semi-online scheduling on two uniform processors
Information Processing Letters
Journal of Combinatorial Optimization
Optimal preemptive semi-online scheduling to minimize makespan on two related machines
Operations Research Letters
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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 驴 1) between the two machines. We show that the greedy algorithm LPT has optimal competitive ratio 1/4(1 +驴17) 驴 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.