Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Primal-Dual Randomized Algorithm for Weighted Paging
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Randomized competitive algorithms for generalized caching
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Primal-dual schema for capacitated covering problems
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
A constant factor approximation algorithm for generalized min-sum set cover
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Universal sequencing on a single machine
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
On the performance of smith's rule in single-machine scheduling with nonlinear cost
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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 following single-machine scheduling problem, which is often denoted 1||Σfj: we are given n jobs to be scheduled on a single machine, where each job j has an integral processing time pj, and there is a nondecreasing, nonnegative cost function fj (Cj) that specifies the cost of finishing j at time Cj; the objective is to minimize n Σj=1n fj (Cj). Bansal & Pruhs recently gave the first constant approximation algorithm and we improve on their 16-approximation algorithm, by giving a primal-dual pseudo-polynomial-time algorithm that finds a solution of cost at most twice the optimal cost, and then show how this can be extended to yield, for any ε 0, a (2 + ε)-approximation algorithm for this problem. Furthermore, we generalize this result to allow the machine's speed to vary over time arbitrarily, for which no previous constant-factor approximation algorithm was known.