A 1.47-approximation algorithm for a preemptive single-machine scheduling problem - Goemans, Michel X.; Wein, Joel M.; Williamson, David P. (Operations research letters, 2000)
In this note, we give a 1.47-approximation algorithm for the preemptive scheduling of jobs with release dates on a single machine so as to minimize the weighted sum of job completion times; this problem is denoted by 1| r j , pmtn|∑ j w j C j in the notation of Lawler et al. (Handbooks in Operations Research and Management Science, Vol. 4, Logistics of Production and Inventory, North-Holland, Amsterdam, pp. 445-522). Our result improves on a 2-approximation algorithm due to Hall et al. Math. Oper. Res. 22 (1997) 513–544, and also yields an improved bound on the quality of a well-known linear programming relaxation of the problem.