Grouping Techniques for Scheduling Problems: Simpler and Faster

Fishkin, Aleksei V.; Jansen, Klaus; Mastrolilli, Monaldo

doi:10.1007/s00453-007-9086-6

Cited by 14 publications

(3 citation statements)

References 22 publications

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“…For those instances where the number of machines and the number of operations per job are constant, Jansen et al [2003] gave a PTAS for the makespan criteria (see also Fishkin et al [2008]). A similar result was obtained by Fishkin et al [2003] for the weighted sum of completion times objective.…”

Section: Literature Reviewmentioning

confidence: 99%

Hardness of Approximating Flow and Job Shop Scheduling Problems

Mastrolilli

Svensson

2011

J. ACM

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We consider several variants of the job shop problem that is a fundamental and classical problem in scheduling. The currently best approximation algorithms have worse than logarithmic performance guarantee, but the only previously known inapproximability result says that it is NP-hard to approximate job shops within a factor less than 5/4. Closing this big approximability gap is a well-known and long-standing open problem.This article closes many gaps in our understanding of the hardness of this problem and answers several open questions in the literature. It is shown the first nonconstant inapproximability result that almost matches the best-known approximation algorithm for acyclic job shops. The same bounds hold for the general version of flow shops, where jobs are not required to be processed on each machine. Similar inapproximability results are obtained when the objective is to minimize the sum of completion times. It is also shown that the problem with two machines and the preemptive variant with three machines have no PTAS.

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Section: Literature Reviewmentioning

confidence: 99%

Hardness of Approximating Flow and Job Shop Scheduling Problems

Mastrolilli

Svensson

2011

J. ACM

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“…It is another open problem [2,16] to understand whether there is a PTAS for the general nonpreemptive and preemptive job shop with a constant number of machines. For those instances where the number of machines and µ are constant, polynomial time approximation schemes are known [9,5] for both, the preemptive and nonpreemptive case.…”

Section: Introductionmentioning

confidence: 99%

(Acyclic) Job Shops are Hard to Approximate

Mastrolilli

Svensson

2008

2008 49th Annual IEEE Symposium on Foundations of Computer Science

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For every > 0, we show that the (acyclic) job shop problem cannot be approximated within ratio O(log 1− lb), unless N P has quasi-polynomial Las-Vegas algorithms, and where lb denotes a trivial lower bound on the optimal value. This almost matches the best known results for acyclic job shops, since an O(log 1+ lb)-approximate solution can be obtained in polynomial time for every > 0.Recently, a PTAS was given for the job shop problem, where the number of machines and the number of operations per job are assumed to be constant. Under P = N P , and when the number µ of operations per job is a constant, we provide an inapproximability result whose value grows with µ to infinity. Moreover, we show that the problem with two machines and the preemptive variant with three machines have no PTAS, unless N P has quasi-polynomial algorithms. These results show that the restrictions on the number of machines and operations per job are necessary to obtain a PTAS.In summary, the presented results close many gaps in our understanding of the hardness of the job shop problem and resolve (negatively) several open problems in the literature.

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“…sets | C max becomes NP-hard in the ordinary sense. Horowitz and Sahni [8], Jansen and Porkolab [11], and Fishkin et al [4] have developed FPTASs for problem Rm | | C max (i.e., problem R | | C max when the number of machines is fixed). Thus, their FPTASs can be applied to problem P m | incl.…”

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confidence: 99%

Scheduling parallel machines with inclusive processing set restrictions and job release times

Wang

2010

European Journal of Operational Research

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We consider the problem of scheduling a set of jobs with different release times on parallel machines so as to minimize the makespan of the schedule. The machines have the same processing speed, but each job is compatible with only a subset of those machines. The machines can be linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process. We present an efficient algorithm for this problem with a worst-case performance ratio of 2. We also develop a polynomial time approximation scheme (PTAS) for the problem, as well as a fully polynomial time approximation scheme (FPTAS) for the case in which the number of machines is fixed.

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Grouping Techniques for Scheduling Problems: Simpler and Faster

Cited by 14 publications

References 22 publications

Hardness of Approximating Flow and Job Shop Scheduling Problems

Hardness of Approximating Flow and Job Shop Scheduling Problems

(Acyclic) Job Shops are Hard to Approximate

Scheduling parallel machines with inclusive processing set restrictions and job release times

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