Semi-normal Schedulings: Improvement on Goemans' Algorithm
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
On the Approximability of Multiprocessor Task Scheduling Problems
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Polynomial time approximation schemes for general multiprocessor job shop scheduling
Journal of Algorithms
On the Complexity of Adjacent Resource Scheduling
Journal of Scheduling
Polynomial time approximation schemes and parameterized complexity
Discrete Applied Mathematics
Enabling rich mobile applications: joint computation and communication scheduling
ACM SIGMOBILE Mobile Computing and Communications Review
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Recently, there have been considerable interests in the multiprocessor job scheduling problem, in which a job can be processed in parallel on one of several alternative subsets of processors. In this paper, a polynomial time approximation scheme is presented for the problem in which the number of processors in the system is a fixed constant. This result is the best possible because of the strong NP-hardness of the problem and is a significant improvement over the past results: the best previous result was an approximation algorithm of ratio $7/6 + \epsilon$ for 3-processor systems based on Goemans's algorithm for a restricted version of the problem.