Scheduling Multiprocessor Tasks to Minimize Schedule Length
IEEE Transactions on Computers
The complexity of scheduling independent two-processor tasks on dedicated processors
Information Processing Letters
Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
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
An approximation algorithm for scheduling on three dedicated machines
Discrete Applied Mathematics
Scheduling independent tasks with multiple modes
Discrete Applied Mathematics - Special volume on partitioning and decomposition in combinatorial optimization
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Polynomial Time Approximation Scheme for General Multiprocessor Job Scheduling
SIAM Journal on Computing
A Simple Linear-Time Approximation Algorithm for Multi-processor Job Scheduling on Four Processors
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Semi-normal Schedulings: Improvement on Goemans' Algorithm
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
On Approximation Scheme Preserving Reducability and Its Applications
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
Scheduling Independent Multiprocessor Tasks
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Hardness of Approximating Problems on Cubic Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Free bits, PCPs and non-approximability-towards tight results
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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The multiprocessor job scheduling problem has received considerable attention recently. An extensive list of approximation algorithms has been developed and studied for the problem under a variety of constraints. In this paper, we show that from the viewpoint of approximability, the general multiprocessor job scheduling problem has a very rich structures such that by putting simple constraints on the number of processors in the system, we can obtain four versions of the problem, which are NP-hard with a fully polynomial time approximation scheme, strongly NP-hard with a polynomial time approximation scheme, APX-complete (thus with a constant approximation ratio in polynomial time), and with no constant approximation ratio in polynomial time, respectively.