A polynomial time approximation scheme for general multiprocessor job scheduling

Recently, there hav been considerable interests in the multiprocessor job s cheduling problem, in which a job can be processed in parallel on one of se veral alternative subsets of processors. In this paper, a polynomial time a pproximation scheme is presented for the problem in which the number of pro cessors 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 impr ovement over the past results: the best previous result was an approximatio n algorithm of ratio 7/6 + epsilon for 3-processor systems based on Goemans 's algorithm for a restricted version of the problem.