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 . We provide an efficient combinatorial 2-approximation algorithm for this problem. In contrast to our work, earlier approximation algorithms  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  has an integrality gap of 2.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics