Non-Preemptive Min-Sum Scheduling with Resource Augmentation

Abstract

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_jF_j (weighted flow time), l |r_j| SigmaT_j (total tardiness), the broadcast version of 1 |r_j| Sigmaw_jF_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_jT_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.