The competitiveness of on-line assignments
Journal of Algorithms
On-Line Load Balancing in a Hierarchical Server Topology
SIAM Journal on Computing
Semi-online scheduling on two uniform processors
Theoretical Computer Science
Online scheduling on two uniform machines to minimize the makespan
Theoretical Computer Science
Online and semi-online scheduling of two machines under a grade of service provision
Operations Research Letters
Hi-index | 5.23 |
We consider the online scheduling of a set of jobs on two uniform machines with the makespan as objective. The jobs are presented in a list. We consider two different eligibility constraint set assumptions, namely (i) arbitrary eligibility constraints and (ii) Grade of Service (GoS) eligibility constraints. In the first case, we prove that the High Speed Machine First (HSF) algorithm, which assigns jobs to the eligible machine that has the highest speed, is optimal. With regard to the second case, we point out an error in [M. Liu et al., Online scheduling on two uniform machines to minimize the makespan, Theoretical Computer Science 410 (21-23) (2009) 2099-2109]; we then provide tighter lower bounds and present algorithms with worst-case analysis for various ranges of machine speeds.