An Approximation Algorithm for Diagnostic Test Scheduling in Multicomputer Systems
IEEE Transactions on Computers
Scheduling multiprocessor tasks on three dedicated processors
Information Processing Letters
Scheduling preemptive multiprocessor tasks on dedicated processors
Performance Evaluation
Complexity of scheduling multiprocessor tasks with prespecified processor allocations
Discrete Applied Mathematics
Deadline scheduling of multiprocessor tasks
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Scheduling computer and manufacturing processes
Scheduling computer and manufacturing processes
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Preemptive open shop scheduling with multiprocessors: polynomial cases and applications
Journal of Scheduling
| Hi-index | 0.00 |
We study the problem of scheduling independent multiprocessor tasks, where for each task in addition to the processing time(s) there is a prespecified dedicated subset (or a family of alternative subsets) of processors which are required to process the task simultaneously. Focusing on problems where all required (alternative) subsets of processors have the same fixed cardinality, we present complexity results for computing preemptive schedules with minimum makespan closing the gap between computationally tractable and intractable instances. In particular, we show that for the dedicated version of the problem, optimal preemptive schedules of bi-processor tasks (i.e., tasks whose dedicated processor sets are all of cardinality two) can be computed in polynomial time. We give various extensions of this result including one to maximum lateness minimization with release times and due dates. All these results are based on a nice relation between preemptive scheduling and fractional coloring of graphs. In contrast to the positive results, we also prove that the problems of computing optimal preemptive schedules for three-processor tasks or for bi-processor tasks with (possible several) alternative modes are strongly NP-hard.