Online computation and competitive analysis
Online computation and competitive analysis
Semi-online scheduling on two uniform processors
Theoretical Computer Science
Online scheduling with reassignment
Operations Research Letters
Online and semi-online scheduling of two machines under a grade of service provision
Operations Research Letters
Semi on-line algorithms for the partition problem
Operations Research Letters
Preemptive on-line scheduling for two uniform processors
Operations Research Letters
Online scheduling on two uniform machines subject to eligibility constraints
Theoretical Computer Science
Online scheduling with reassignment on two uniform machines
Theoretical Computer Science
Online scheduling with rearrangement on two related machines
Theoretical Computer Science
Optimal semi-online algorithms for scheduling problems with reassignment on two identical machines
Information Processing Letters
Optimal algorithms for online scheduling with bounded rearrangement at the end
Theoretical Computer Science
Online scheduling with rejection and withdrawal
Theoretical Computer Science
Online scheduling with one rearrangement at the end: Revisited
Information Processing Letters
Online minimum makespan scheduling with a buffer
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Semi-online hierarchical scheduling problems with buffer or rearrangements
Information Processing Letters
Semi-online scheduling with two GoS levels and unit processing time
Theoretical Computer Science
Hi-index | 5.23 |
We consider two problems of online scheduling on two uniform machines: online scheduling under a grade of service (GoS) and online scheduling with reassignment. These problems are online in the sense that when a job presents, we have to irrevocably assign it to one of the machines before the next job is seen. The objective is to minimize the makespan. In the first problem, GoS means that some jobs have to be processed by some machine so that they can be guaranteed a higher quality. Assume that the speed of the higher GoS machine is normalized to 1, while the speed of the other one is s. We show that a lower bound of competitive ratio is 1+2ss+2 in the case 01. Then we propose and analyze two online algorithms: HSF algorithm and EX-ONLINE algorithm. HSF is optimal in the case where s1 and @S"1=@S"2s, where @S"1 and @S"2 denote the total processing time of jobs which request higher GoS machine and the total processing time of jobs which request the normal one, respectively. EX-ONLINE is optimal in the case 2(2-1)@?s@?1. In the second problem, we study two subproblems P"L and P"A proposed in [Z. Tan, S. Yu, Online scheduling with reassignment, Operations Research Letters 36 (2008) 250-254]. Assume that the speeds of 2 uniform machines are 1 and s=1, respectively. For P"L where we can reassign the last k jobs of the sequence, we show a lower bound of competitive ratio 1+11+s. For P"A where we can reassign arbitrary k jobs, we show a lower bound of competitive ratio (s+1)^2s^2+s+1. We propose a s+1s-competitive algorithm HSF-1 for both P"L and P"A. For P"A, we propose a (s+1)^2s+2-competitive algorithm EX-RA, which is superior to HSF-1 when 1@?s@?2.