A Fast Algorithm for Multiprocessor Scheduling of Unit-Length Jobs

An efficient polynomial time algorithm for the problem of scheduling n unit length jobs with rational release times and deadlines on m identical parallel machines is presented. By using preprocessing, a running time of $O(mn^2 )$ is obtained that is an improvement over the previous best running time of $O(n^3 \log \log n)$. The authors also present new NP-completeness results for two closely related problems.