Minimizing Total Flow-Time: The Unrelated Case

Garg, Naveen; Kumar, Amit; Muralidhara, V. N.

doi:10.1007/978-3-540-92182-0_39

Cited by 14 publications

(18 citation statements)

References 6 publications

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“…One another nice property of our algorithm is that it dispatches a job to the appropriate machine as soon as the job arrives. We would like to point out that in the absence of speed augmentation we do not even know of any approximation algorithm (with non-trivial guarantees) for the problem of minimizing flow time on unrelated machines [13].…”

Section: Introductionmentioning

confidence: 99%

A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentation

Chadha

Garg

Kumar

et al. 2009

Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing

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We consider the online problem of scheduling jobs on unrelated machines so as to minimize the total weighted flow time. This problem has an unbounded competitive ratio even for very restricted settings. In this paper we show that if we allow the machines of the online algorithm to have more speed than those of the offline algorithm then we can get an O((1 + −1 ) 2 )-competitive algorithm.Our algorithm schedules jobs preemptively but without migration. However, we compare our solution to an offline algorithm which allows migration. Our analysis uses a potential function argument which can also be extended to give a simpler and better proof of the randomized immediate dispatch algorithm of Chekuri-Goel-Khanna-Kumar for minimizing average flow time on parallel machines.

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Section: Introductionmentioning

confidence: 99%

A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentation

Chadha

Garg

Kumar

et al. 2009

Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing

Self Cite

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“…Before describing the new LP formulation that we use, we describe the standard time-indexed linear programming relaxation for the problem that was used, for example, in [15,16].…”

Section: Alternate Lp Relaxation and The High-level Ideamentioning

confidence: 99%

“…Here, P denotes the ratio of maximum processing length of jobs to the minimum processing length. Using a standard trick this implies an O(log 2 n) approximation, which may be better if P is super-polynomial in n. An approximation hardness of Ω(log P ) is also known for the problem even in the much simpler setting of identical machines [16]. Theorem 1.2.…”

Section: Introductionmentioning

confidence: 99%

“…In an important breakthrough, Garg and Kumar [15] gave a O(log P ) approximation, based on an elegant and non-trivial LP rounding approach. They consider a natural LP relaxation of the problem, and round it based on computing certain unsplittable flows [11] on an appropriately defined graph.To extend these ideas to the unrelated machines case, [16] introduce a (α, β)-variability setting (see [16] for details) and prove a general result that implies logarithmic approximations for both restricted assignment and related machines setting. For the unrelated setting, their result gives an O(k) approximation where k is the number of different possible values of p ij in the instance.…”

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confidence: 99%

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Minimizing Flow-Time on Unrelated Machines

Bansal

Kulkarni

2015

Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing

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We consider some classical flow-time minimization problems in the unrelated machines setting. In this setting, there is a set of m machines and a set of n jobs, and each job j has a machine dependent processing time of p ij on machine i. The flow-time of a job is the amount of time the job spends in a system (its completion time minus its arrival time), and is one of the most natural measures of quality of service. We show the following two results: an O(min(log 2 n, log n log P )) approximation algorithm for minimizing the total flow-time, and an O(log n) approximation for minimizing the maximum flowtime. Here P is the ratio of maximum to minimum job size. These are the first known poly-logarithmic guarantees for both the problems.

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“…The unrelated machines model can also be used when different map machines have different amounts of memory and each task carries a minimum memory requirement to run. There is a large amount of literature on the unrelated machines model in scheduling theory and this is perhaps the most general machine model (see [14,15,4,18,32]). Our results.…”

Section: Introductionmentioning

confidence: 99%

On scheduling in map-reduce and flow-shops

Moseley

Dasgupta

Kumar

et al. 2011

Proceedings of the Twenty-Third Annual ACM Symposium on Parallelism in Algorithms and Architectures

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The map-reduce paradigm is now standard in industry and academia for processing large-scale data. In this work, we formalize job scheduling in map-reduce as a novel generalization of the two-stage classical flexible flow shop (FFS) problem: instead of a single task at each stage, a job now consists of a set of tasks per stage. For this generalization, we consider the problem of minimizing the total flowtime and give an efficient 12-approximation in the offline setting and an online (1 + Motivated by map-reduce, we revisit the two-stage flow shop problem, where we give a dynamic program for minimizing the total flowtime when all jobs arrive at the same time. If there are fixed number of job-types the dynamic program yields a PTAS; it is also a QPTAS when the processing times of jobs are polynomially bounded. This gives the first improvement in approximation of flowtime for the two-stage flow shop problem since the trivial 2-approximation algorithm of Gonzalez and Sahni [29] in 1978, and the first known approximation for the FFS problem. We then consider the generalization of the two-stage FFS problem to the unrelated machines case, where we give an offline 6-approximation and an online (1 + )-speed O( 1 4 )-competitive algorithm.

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Minimizing Total Flow-Time: The Unrelated Case

Cited by 14 publications

References 6 publications

A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentation

A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentation

Minimizing Flow-Time on Unrelated Machines

On scheduling in map-reduce and flow-shops

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