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 minimizing sum of weighted completion times. The problem is NP-hard when there are precedence constraints between jobs 15]. We provide an eecient com-binatorial 2-approximation algorithm for this problem. In contrast to our work, earlier approximation algorithms 12] achieving constant factor approximations are based on solving a linear programming relaxation of the problem. We also show that the linear ordering relaxation of Potts 20] has an integrality gap of 2.