A Polynomial Approximation Scheme for Scheduling on Uniform Processors: Using the Dual Approximation Approach

• Published in: SIAM journal on computing Vol. 17; no. 3; pp. 539 - 551
• Main Authors: Hochbaum, Dorit S., Shmoys, David B.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.06.1988
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Approximation; Computer science; control theory; systems; Employment; Exact sciences and technology; Job shops; Packing problem; Scheduling; Theoretical computing; Multiprocessor; Parallel processing; Approximation; Integrated planning; Algorithm analysis; Polynomial time
• ISSN: 0097-5397; 1095-7111
• DOI: 10.1137/0217033

We present a polynomial approximation scheme for the minimum makespan problem on uniform parallel processors. More specifically, the problem is to find a schedule for a set of independent jobs on a collection of machines of different speeds so that the last job to finish is completed as quickly as possible. We give a family of polynomial-time algorithms $\{ {A_\varepsilon } \}$ such that $A_\varepsilon $ delivers a solution that is within a relative error $\varepsilon $ of the optimum. This is a dramatic improvement over previously known algorithms; the best performance guarantee previously proved for a polynomial-time algorithm ensured a relative error no more than 40 percent. The technique employed is the dual approximation approach, where infeasible but superoptimal solutions for a related (dual) problem are converted to the desired feasible but possibly suboptimal solution.