Minimizing mean flow time with release time constraint
Theoretical Computer Science
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
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
Algorithms for minimizing weighted flow time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimizing the Flow Time Without Migration
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Developments from a June 1996 seminar on Online algorithms: the state of the art
Minimizing total flow time and total completion time with immediate dispatching
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Minimizing flow time nonclairvoyantly
Journal of the ACM (JACM)
Online Scheduling to Minimize Average Stretch
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Average stretch without migration
Journal of Computer and System Sciences
Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines
Journal of the ACM (JACM)
Minimizing Average Flow Time in Sensor Data Gathering
Algorithmic Aspects of Wireless Sensor Networks
Minimizing Average Flow Time on Unrelated Machines
Approximation and Online Algorithms
Scalably scheduling power-heterogeneous processors
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Minimizing flow time in the wireless gathering problem
ACM Transactions on Algorithms (TALG)
On scheduling in map-reduce and flow-shops
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
An online scalable algorithm for minimizing lk-norms of weighted flow time on unrelated machines
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Online scheduling on identical machines using SRPT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Improved multi-processor scheduling for flow time and energy
Journal of Scheduling
Nonclairvoyant sleep management and flow-time scheduling on multiple processors
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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We consider the problem of optimizing the total flow time of a stream of jobs that are released over time in a multiprocessor setting. This problem is NP-hard even when there are only two machines and preemption is allowed. Although the total (or average) flow time is widely accepted as a good measurement of the overall quality of service, no approximation algorithms were known for this basic scheduling problem. This paper contains two main results. We first prove that when preemption is allowed, Shortest Remaining Processing Time (SRPT) is an O(log(min{nm,P})) approximation algorithm for the total flow time, where n is the number of jobs, m is the number of machines, and P is the ratio between the maximum and the minimum processing time of a job. We also provide an @W(log(nm+P)) lower bound on the (worst case) competitive ratio of any randomized algorithm for the on-line problem in which jobs are known at their release times. Thus, we show that up to a constant factor SRPT is an optimal on-line algorithm. Our second main result addresses the non-preemptive case. We present a general technique that allows to transform any preemptive solution into a non-preemptive solution at the expense of an O(nm) factor in the approximation ratio of the total flow time. Combining this technique with our previous result yields an O(nmlognm) approximation algorithm for this case. We also show an @W(n^1^3^-^@e) lower bound on the approximability of this problem (assuming PNP).