On Scheduling Independent Tasks with Restricted Execution Times
Operations Research · 1982 · Volume 30 · Issue 1
Abstract
We consider the problem of nonpreemptively scheduling n independent tasks on m identical and parallel machines with the objective of minimizing the overall finishing time. The problem has been shown to be NP-complete in the strong sense and hence there probably will not be any pseudopolynomial time algorithm for solving this problem. We show, however, that if the execution times are restricted to a fixed number, say k , of different values, then it can be solved in polynomial time. Our algorithm can be implemented to run in time 0(log 2 p * log 2 m * n 2( k −1) ) and space 0(log 2 m * n k −1 ) in the worst case, where p is the largest execution time.
Keywords
111 dynamic programming method, 584 deterministic scheduling theory
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