Formulating the single machine sequencing problem with release dates as a mixed integer program
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Approximability and nonapproximability results for minimizing total flow time on a single machine
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximating total flow time on parallel machines
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Scheduling to minimize average stretch without migration
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Algorithms for minimizing weighted flow time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Improved algorithms for stretch scheduling
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A Supermodular Relaxation for Scheduling with Release Dates
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Online Scheduling to Minimize Average Stretch
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Server scheduling in the Lp norm: a rising tide lifts all boat
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Non-clairvoyant scheduling for weighted flow time
Information Processing Letters
Approximation Algorithms for Average Stretch Scheduling
Journal of Scheduling
On minimizing the total flow time on multiple machines
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Multi-processor scheduling to minimize flow time with ε resource augmentation
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Designing PTASs for MIN-SUM scheduling problems
Discrete Applied Mathematics - Special issue: Efficient algorithms
Minimizing the stretch when scheduling flows of biological requests
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
ACM Transactions on Algorithms (TALG)
Minimizing the stretch when scheduling flows of divisible requests
Journal of Scheduling
Weighted flow time does not admit O(1)-competitive algorithms
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Fair, effective, efficient and differentiated scheduling in an enterprise data warehouse
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
Server Scheduling to Balance Priorities, Fairness, and Average Quality of Service
SIAM Journal on Computing
Minimizing flow time on a constant number of machines with preemption
Operations Research Letters
The complexity of scheduling for p-norms of flow and stretch
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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(MATH) We present the first approximation schemes for minimizing weighted flow time on a single machine with preemption. Our first result is an algorithm that computes a (1+&egr;)-approximate solution for any instance of weighted flow time in O(nO(ln W ln P/&egr;3)) time; here P is the ratio of maximum job processing time to minimum job processing time, and W is the ratio of maximum job weight to minimum job weight. This result directly gives a quasi-PTAS for weighted flow time when P and W are poly-bounded, and a PTAS when they are both O(1). We strengthen the former result to show that in order to get a quasi- PTAS it suffices to have just one of P and W to be poly-bounded. Our result provides strong evidence to the hypothesis that the weighted flow time problem has a PTAS. We note that the problem is strongly NP-hard even when P and W are O(1). We next consider two important special cases of weighted flow time, namely, when P is O(1) and W is arbitrary, and when the weight of a job is inverse of its processing time referred to as the stretch metric. For both of the above special cases we obtain a (1+&egr;)-approximation for any &egr; ρ 0 by using a randomized partitioning scheme to reduce an arbitrary instance to several instances all of which have P and W bounded by a constant that depends only on &egr;.