Non-Preemptive Min-Sum Scheduling with Resource Augmentation

We give the first O(l)-speed O(l) approximation polynomial-time algorithms for several nonpreemptive min-sum scheduling problems where jobs arrive over time and must be processed on one machine. More precisely, we give the first O(l)-speed O(l)-approximations for the non-preemptive scheduling problems; l|r
_j
| Sigmaw
_j
F
_j
(weighted flow time), l |r
_j
| SigmaT
_j
(total tardiness), the broadcast version of 1 |r
_j
| Sigmaw
_j
F
_j
, an O(I)-speed, 1-approximation for l |r
_j
| Sigma U macr
_j
(throughput maximization), and an O(l)-machine, O(l)-speed O(1)-approximation for l |r
_j
| Sigmaw
_j
T
_j
(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.