Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On-Line Load Balancing in a Hierarchical Server Topology
SIAM Journal on Computing
Scheduling unit length jobs with parallel nested machine processing set restrictions
Computers and Operations Research
Parallel machine scheduling with nested job assignment restrictions
Operations Research Letters
An optimal rounding gives a better approximation for scheduling unrelated machines
Operations Research Letters
| Hi-index | 5.23 |
We consider the problem of scheduling n independent jobs on m parallel machines, where the machines differ in their functionality but not in their processing speeds. Each job has a restricted set of machines to which it can be assigned, called its processing set. Preemption is not allowed. Our goal is to minimize the makespan of the schedule. We study two variants of this problem: (1) the case of tree-hierarchical processing set and (2) the case of nested processing set. We first give a fast algorithm for the case of tree-hierarchical processing set with a worst-case bound of 4/3, which is better than the best known algorithm whose worst-case bound is 2. We then give a more complicated algorithm for the case of nested processing set with a worst-case bound of 5/3, which is better than the best known algorithm whose worst-case bound is 7/4. In both cases, we will give examples achieving the worst-case bounds.