Approximation schemes for minimizing average weighted completion time with release dates

Afrati, Foto N.; Bampis, Evripidis; Chekuri, Chandra; Karger, David R.; Kenyon, Claire; Khanna, Sanjeev; Milis, Ioannis; Queyranne, Maurice; Skutella, Martin; Stein, Clifford; Sviridenko, Maxim

doi:10.1109/sffcs.1999.814574

Cited by 116 publications

(206 citation statements)

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“…Similarly the set of nonzero β S variables constitute a feasible solution. Since any convex combination of two feasible solutions yields a feasible solution, by scaling the α j variables by a factor of 2 3 and the β S variables by a factor of 1 3 we obtain a new feasible solution. Since any dual feasible solution is a lower bound on OP T the claim follows.…”

Section: Discussionmentioning

confidence: 99%

“…In the offline case, the algorithm has complete knowledge of all jobs when constructing the schedule, however, in the online setting, we gain knowledge of a job on its release date and for each time t we must construct the schedule until time t without any knowledge of jobs that are released afterwards. For the offline problem, polynomial time approximation schemes have been developed [1]. There are also several linear programming based approximations [3,4,7,10,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

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Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine

Davis

Gandhi

Kothari

2013

Operations Research Letters

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We study the problem of minimizing the weighted sum of completion times of jobs with release dates on a single machine with the aim of shedding new light on "the simplest [linear program] relaxation" [17]. Specifically, we analyze a 3-competitive online algorithm [16], using dual-fitting. In the offline setting, we develop a primal-dual algorithm with approximation guarantee 1 + √ 2. The latter implies that the cost of the optimal schedule is within a factor of 1 + √ 2 of the cost of the optimal LP solution.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine

Davis

Gandhi

Kothari

2013

Operations Research Letters

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“…This is true even on a single processor or if all release dates are equal. Polynomial time approximation schemes have been presented by Afrati et al [1].…”

Section: Previous Workmentioning

confidence: 99%

A Tight 2-Approximation for Preemptive Stochastic Scheduling

Megow

Vredeveld

2014

Mathematics of OR

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We consider dynamic stochastic scheduling of preemptive jobs with processing times that follow independent discrete probability distributions. We derive a policy with a guaranteed performance ratio of 2 for the problem of minimizing the sum of weighted completion times on identical parallel machines subject to release dates. The analysis is tight. Our policy as well as their analysis applies also to the more general model of stochastic online scheduling.In contrast to previous results for nonpreemptive stochastic scheduling, our preemptive policy yields an approximation guarantee that is independent of the processing time distributions. However, our policy extensively utilizes information on the distributions other than the first (and second) moments. We also introduce a new nontrivial lower bound on the expected value of an unknown optimal policy. It relies on a relaxation to the basic problem on a single machine without release dates, which is known to be solved optimally by the Gittins index priority rule. This dynamic priority index is crucial to the analysis and also inspires the design of our policy.Keywords: scheduling; stochastic; approximation algorithm; total weighted completion time MSC2000 subject classification: Primary: 90B36; secondary: 68W40 OR/MS subject classification: Primary: production/scheduling; secondary: approximation/heuristic History: Received August 15, 2011; revised March 9, 2014. Published online in Articles in Advance.1. Introduction. Stochastic scheduling problems have attracted researchers for about four decades. A full range of articles is concerned with criteria that guarantee the optimality of simple policies for special scheduling problems; see, e.g., Pinedo [26]. It is only recently that research also focuses on approximations for less restrictive problem settings (Möhring et al. All these results apply to nonpreemptive scheduling, and we are not aware of any approximation results when job preemption is allowed and processing times are stochastic.In this paper, we give the first constant factor approximation for the stochastic version of the classical problem of scheduling jobs preemptively, with or without release dates, on identical parallel machines. The objective is to minimize the expected sum of weighted completion times.We provide a very natural scheduling policy and show that it has an expected objective value of at most twice the expected optimal value. The analysis of our policy is tight. Both, the policy and its analysis are also valid in the model of stochastic online scheduling (Megow et al. [19], Chou et al. [5], Vredeveld [39]). They rely on the celebrated Gittins index priority rule (Gittins [9, 10]), which is an optimal policy for the setting when there is only one machine and there are no nontrivial release dates (Sevcik [33], Weiss [41]). Under deterministic input, our policy corresponds to the preemptive weighted shortest processing time (WSPT) rule, which is known to have a tight performance guarantee of 2 on identical parallel machines (Megow and Schulz...

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“…A QPTAS with running time n O ε (log P log W ) is also known [13]. For the objective of minimizing the weighted sum of completion times, PTASs are known, even for an arbitrary number of identical and a constant number of unrelated machines [1].…”

Section: Related Workmentioning

confidence: 99%

“…Some of them are already very well understood, for instance weighted sum of completion times j w j C j for which there are polynomial time approximation schemes (PTASs) [1], even for multiple machines and very general machine models. On the other hand, for natural and important objectives such as weighted flow time or weighted tardiness, not even a constant factor polynomial time approximation algorithm is known, even on a single machine.…”

Section: Introductionmentioning

confidence: 99%

How Unsplittable-Flow-Covering Helps Scheduling with Job-Dependent Cost Functions

Höhn

Mestre

Wiese

2014

Automata, Languages, and Programming

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Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private cost function, and one seeks to schedule the jobs to minimize the total sum of these costs. The framework captures many important scheduling objectives such as weighted flow time or weighted tardiness. Still, the general case as well as the mentioned special cases are far from being very well understood yet, even for only one machine. Aiming for better general understanding of this problem, in this paper we focus on the case of uniform job release dates on one machine for which the state of the art is a 4-approximation algorithm. This is true even for a special case that is equivalent to the covering version of the well-studied and prominent unsplittable flow on a path problem, which is interesting in its own right. For that covering problem, we present a quasi-polynomial time (1 + ε)-approximation algorithm that yields an (e + ε)-approximation for the above scheduling problem. Moreover, for the latter we devise the best possible resource 123Algorithmica augmentation result regarding speed: a polynomial time algorithm which computes a solution with optimal cost at 1 + ε speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most log n many classes. This algorithm allows the jobs even to have up to log n many distinct release dates. All proposed quasi-polynomial time algorithms require the input data to be quasi-polynomially bounded.

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Approximation schemes for minimizing average weighted completion time with release dates

Cited by 116 publications

References 24 publications

Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine

Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine

A Tight 2-Approximation for Preemptive Stochastic Scheduling

How Unsplittable-Flow-Covering Helps Scheduling with Job-Dependent Cost Functions

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