Non-preemptive min-sum scheduling with resource augmentation

We give the first O(1)-speed O(1)-approximation polynomial-time algorithms for several nonpreemptive minsum scheduling problems where jobs arrive over time and must be processed on one machine. More precisely, we give the first O(1)-speed O(1)-approximations for the non-preemptive scheduling problems 1 | rj | Σ wjFj (weighted flow time), | rj | Σ Tj (total tardiness), the broadcast version, of 1 | rj | Σ wjFj, an O(1)-speed, 1-approximation for 1 | rj | ΣŪj (throughput maximization), and an O(1)-machine, O(1)-speed O(1)-approximation for 1 | r j | Σ wj Tj (weighted tardiness). Our main, contribution is an integer programming formulation whose relaxation is sufficiently close to the integer optimum, and which can be transformed to a schedule on a faster machine. © 2007 IEEE.