`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications
Journal of the ACM (JACM)
On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming
Journal of the ACM (JACM)
Scheduling independent tasks to reduce mean finishing time
Communications of the ACM
Minimizing Total Completion Time on Parallel Machines with Deadline Constraints
SIAM Journal on Computing
Minimizing the stretch when scheduling flows of divisible requests
Journal of Scheduling
Preemptive scheduling on uniform machines to minimize mean flow time
Computers and Operations Research
| Hi-index | 0.00 |
We show that the problems of minimizing total completion time and of minimizing the number of late jobs on unrelated parallel machines, when preemption is allowed, are both NP-hard in the strong sense. The former result settles a long-standing open question and is remarkable since the non-preemptive version is known to be solvable in polynomial time. A special case of the unrelated machine model is the identical machine model with the restriction that a job can only be processed on a specific subset of the machines. We show that in this model the problem of minimizing total completion time. When preemption is allowed, can be solved in polynomial time by proving that the use of preemption is redundant.