Efficient Algorithms for Average Completion Time Scheduling

Sitters, René

doi:10.1007/978-3-642-13036-6_31

Cited by 16 publications

(16 citation statements)

References 23 publications

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“…This algorithm has been generalized further to the multiple-machine problem without loss of performance in Megow and Schulz [18]. Sitters [36] presented a deterministic online algorithm with a performance guarantee of 1 791 1 + 1/ √ m 2 , which is less than 2 for m ≥ 311 and drops to 1 791 if m tends to infinity. Combining it with the randomized 2 − 1/m -competitive algorithm by Correa and Wagner [7], Sitters obtains an improved randomized online algorithm for parallel machines.…”

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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Section: Previous Workmentioning

confidence: 99%

A Tight 2-Approximation for Preemptive Stochastic Scheduling

Megow

Vredeveld

2014

Mathematics of OR

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“…While our result for WSRPT does not beat the competitiveness of the best known algorithm for the problem P | r j , pmtn | j w j c j (which is due to [6]), our contribution is with respect to the WSRPT algorithm and techniques for analyzing the algorithm as applied to parallel machines. While the algorithm itself is simple to state, it has proven somewhat difficult to analyze, due to the interplay of the static job weights with the changing nature of the remaining processing times.…”

Section: Introductionmentioning

confidence: 99%

“…At every point in time, SRPT simply schedules the m jobs with shortest remaining processing time. SRPT is known to be 5/4-competitive for the unweighted variant of the problem [6]. WSRPT can be seen as the weighted version of SRPT.…”

Section: Wsrptmentioning

confidence: 99%

“…With respect to upperbounds, for weighted completion time scheduling, Megow and Schulz [5] showed that the algorithm WSPT (Weighted Shortest Processing Time), which schedules jobs in order of non-decreasing weight-to-size ratio, is 2-competitive. Sitters [6] then recently gave an algorithm that is 1.791-competitive for weighted completion time scheduling.…”

Section: Introductionmentioning

confidence: 99%

“…The competitiveness of SRPT for parallel machines was first analyzed in 1995 by [7], has been evaluated experimentally (e.g., [8][9][10]), and has continued to be widely used and studied. It was a long-held belief that SRPT was close to optimal, and most recently, [6] finally showed that SRPT is 5/4-competitive. (Prior to that, the original proof of SRPT's 2-competitiveness [7] was the best known ratio for fifteen years until [11] showed it was 1.86-competitive.)…”

Section: Introductionmentioning

confidence: 99%

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Completion Time Scheduling and the WSRPT Algorithm

Xiong

Chung

2012

Lecture Notes in Computer Science

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Abstract. We consider the online scheduling problem of minimizing the total weighted and unweighted completion time on identical parallel machines with preemptible jobs. We show a new general lower bound of 21/19 ≈ 1.105 on the competitive ratio of any deterministic online algorithm for the unweighted problem and 16− √ 14 11 ≈ 1.114 for the weighted problem. We then analyze the performance of the natural online algorithm WSRPT (Weighted Shortest Remaining Processing Time). We show that WSRPT is 2-competitive. We also prove that the lower bound on the competitive ratio of WSRPT for this problem is 1.215.

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Online and Semi-online Scheduling

Tan

Zhang

2013

Handbook of Combinatorial Optimization

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Efficient Algorithms for Average Completion Time Scheduling

Cited by 16 publications

References 23 publications

A Tight 2-Approximation for Preemptive Stochastic Scheduling

A Tight 2-Approximation for Preemptive Stochastic Scheduling

Completion Time Scheduling and the WSRPT Algorithm

Online and Semi-online Scheduling

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