Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Server Scheduling to Balance Priorities, Fairness, and Average Quality of Service
SIAM Journal on Computing
A primal-dual approximation algorithm for min-sum single-machine scheduling problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Universal sequencing on a single machine
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Dual techniques for scheduling on a machine with varying speed
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
| Hi-index | 0.00 |
We consider the problem of scheduling jobs on a single machine. Given some continuous cost function, we aim to compute a schedule minimizing the weighted total cost, where the cost of each individual job is determined by the cost function value at the job's completion time. This problem is closely related to scheduling a single machine with nonuniform processing speed. We show that for piecewise linear cost functions it is strongly NP-hard. The main contribution of this article is a tight analysis of the approximation factor of Smith's rule under any particular convex or concave cost function. More specifically, for these wide classes of cost functions we reduce the task of determining a worst case problem instance to a continuous optimization problem, which can be solved by standard algebraic or numerical methods. For polynomial cost functions with positive coefficients it turns out that the tight approximation ratio can be calculated as the root of a univariate polynomial. To overcome unrealistic worst case instances, we also give tight bounds that are parameterized by the minimum, maximum, and total processing time.