Non-preemptive Scheduling on Machines with Setup Times

Mäcker, Alexander; Malatyali, Manuel; Heide, Friedhelm Meyer auf der; Riechers, Sören

doi:10.1007/978-3-319-21840-3_45

Cited by 8 publications

(8 citation statements)

References 14 publications

(24 reference statements)

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“…In the following, we use the term α-approximation as an abbreviation for polynomial time algorithms with approximation guarantee α. The setup class model was first considered by Mäcker et al [29] in the special case that all classes have the same setup time. They designed a 2-approximation and additionally a (3/2 + ε)-approximation for the case that the overall length of the jobs from each class is bounded.…”

Section: Related Workmentioning

confidence: 99%

Empowering the configuration-IP: new PTAS results for scheduling with setup times

et al. 2021

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Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems where a set of items has to be placed in multiple target locations. Herein, a configuration describes a possible placement on one of the target locations, and the IP is used to choose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and, therefore, be solved efficiently. As an application, we consider scheduling problems with setup times in which a set of jobs has to be scheduled on a set of identical machines with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed, an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time $$f(1/\varepsilon )\cdot \mathrm {poly}(|I|)$$ f ( 1 / ε ) · poly ( | I | ) . Previously, only constant factor approximations of 5/3 and $$4/3 + \varepsilon $$ 4 / 3 + ε , respectively, were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine.

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Section: Related Workmentioning

confidence: 99%

Empowering the configuration-IP: new PTAS results for scheduling with setup times

et al. 2021

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“…More recently Mäcker et al [7] made progress to the case of nonpreemptive scheduling. They used the restrictions that all setup times are equal (s i = s) and the total processing time of each class is bounded by γ OPT for some constant γ , i.e.…”

Section: Introductionmentioning

confidence: 99%

“…s i + j ∈C i t j ≤ OPT. Most suitable for this kind of problems, they found a heuristic that first uses list scheduling for complete batches followed by an attempt of splitting some batches m variable m fixed unrestricted small batches or |C i | = 1 or P(C i ) ≤ γ OPT Splittable 5/3 in poly [12] 3/2 in O(n + c log(c + m)) * EPTAS [5] ≈ 3 2 in O(n + (m + c) log(m + c)) [1] FPTAS [12] Non-Preemptive 2 + ε in O(n log 1/ε), PTAS [6] 3/2 in O(n log(n + ∆)) * EPTAS [5] (1 + ε) min { 3 2 OPT, OPT +t max − 1 } in poly [7] FPTAS [7] Preemptive (2 − (⌊m/2⌋ + 1) −1 ) in O(n) [10] 3/2 in O(n logn) * 4/3 + ε in poly [11] EPTAS [5] / Table 1: An overview of known results * Result is in this paper so that they are scheduled on two different machines. This second approach needs a running time of O(n + (m +c)log(m +c)) and considering only small batches it is ( 3 2 − 1 4m−4 )-approximate if m ≤ 4 whereas it is ( 53 − 1 m )-approximate for small batches if m is a multiple of 3 and m ≥ 6.…”

Section: Introductionmentioning

confidence: 99%

Near-Linear Approximation Algorithms for Scheduling Problems with Batch Setup Times

Deppert

Jansen

2019

The 31st ACM Symposium on Parallelism in Algorithms and Architectures

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We investigate the scheduling of n jobs divided into c classes on m identical parallel machines. For every class there is a setup time which is required whenever a machine switches from the processing of one class to another class. The objective is to find a schedule that minimizes the makespan. We give near-linear approximation algorithms for the following problem variants: the non-preemptive context where jobs may not be preempted, the preemptive context where jobs may be preempted but not parallelized, as well as the splittable context where jobs may be preempted and parallelized.We present the first algorithm improving the previously best approximation ratio of 2 to a better ratio of 3/2 in the preemptive case. In more detail, for all three flavors we present an approximation ratio 2 with running time O(n), ratio 3/2 + ε in time O(n log 1/ε) as well as a ratio of 3/2. The (3/2)-approximate algorithms have different running times. In the non-preemptive case we get time O(n log(n + ∆)) where ∆ is the largest value of the input. The splittable approximation runs in time O(n + c log(c + m)) whereas the preemptive algorithm has a running time O(n log(c + m)) ≤ O(n log n). So far, no PTAS is known for the preemptive problem without restrictions, so we make progress towards that question. Recently Jansen et al. found an EPTAS for the splittable and nonpreemptive case but with impractical running times exponential in 1/ε.

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“…They design a (1 + φ)-approximation, where φ ≈ 1.618 is the golden ratio, for the case of unrelated machines as well as an inapproximability result of e e−1 . The model with classes and (class-independent) setups was first considered by Mäcker et al for identical machines in [24], where constant factor approximations are presented. In [18], Jansen and Land improve upon these results by providing a PTAS (even) for the case of class-dependent setup times.…”

Section: Related Workmentioning

confidence: 99%

Scheduling on (Un-)Related Machines with Setup Times

Jansen

Maack

Mäcker

2019

2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

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We consider a natural generalization of scheduling n jobs on m parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches from processing jobs of one class to jobs of a different class. During such a setup, a machine cannot process jobs and the duration of a setup may depend on the machine as well as the class of the job to be processed next.For this problem, we study approximation algorithms for non-identical machines. We develop a polynomial-time approximation scheme for uniformly related machines. For unrelated machines we obtain an O(log n + log m)-approximation, which we show to be optimal (up to constant factors) unless N P ⊂ RP . We also identify two special cases that admit constant factor approximations.

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Non-preemptive Scheduling on Machines with Setup Times

Cited by 8 publications

References 14 publications

Empowering the configuration-IP: new PTAS results for scheduling with setup times

Empowering the configuration-IP: new PTAS results for scheduling with setup times

Near-Linear Approximation Algorithms for Scheduling Problems with Batch Setup Times

Scheduling on (Un-)Related Machines with Setup Times

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