Precedence Constrained Scheduling to Minimize Sum of Weighted Completion Times on a Single Machine

We consider the problem of scheduling a set of jobs on a single machine with the objective of mimizing weighted (average) completion time. The problem is NP-hard when there are precedence constraints between jobs, [12] and we provide a simple and efficient combinatorial 2-approximation algorithm. In contrast to our work, earlier approximation altorithms [9] achieving the same ratio are based on solving a linear programming relaxation of the problem.

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