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A Note on NP-Hardness of Preemptive Mean Flow-Time Scheduling for Parallel Machines [article]

Odile Bellenguez-Morineau, Marek Chrobak, Christoph Dürr, Damien Prot
2014 arXiv   pre-print
We point out a serious error in their proof and give a new proof of strong NP-hardness for this problem.  ...  In the paper "The complexity of mean flow time scheduling problems with release times", by Baptiste, Brucker, Chrobak, Dürr, Kravchenko and Sourd, the authors claimed to prove strong NP-hardness of the  ...  The authors would like to thank anonymous reviewers for many useful comments and suggestions.  ... 
arXiv:1404.5424v1 fatcat:axj6w4fgmzcftbdfdxgl2ii7pa

A note on $${\mathbb {NP}}$$ NP -hardness of preemptive mean flow-time scheduling for parallel machines

Odile Bellenguez-Morineau, Marek Chrobak, Christoph Dürr, Damien Prot
2014 Journal of Scheduling  
We point out a serious error in their proof and give a new proof of strong NP-hardness for this problem.  ...  In the paper "The complexity of mean flow time scheduling problems with release times", by Baptiste, Brucker, Chrobak, Dürr, Kravchenko and Sourd, the authors claimed to prove strong NP-hardness of the  ...  The authors would like to thank anonymous reviewers for many useful comments and suggestions.  ... 
doi:10.1007/s10951-014-0380-2 fatcat:sartoaygbnct7fseckxt26iymq

Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard

J.A. Hoogeveen, J.K. Lenstra, B. Veltman
1996 European Journal of Operational Research  
We show that preemptive scheduling in a two-stage flow shop with at least two identical parallel machines in one of the stages so as to minimize makespan is NP-hard in the strong sense. 1991 Mathematics  ...  McNaughton's wrap-around Nle [1959] finds a shortest preemptive schedule on identical parallel machines in Unear time.  ...  In this note. we will show that preemptive scheduling in a two-stage flow shop with at least two identical parallel machines in one of the stages so as to minimize makespan is NP-hard in the strong sense  ... 
doi:10.1016/s0377-2217(96)90070-3 fatcat:u2oly4cm2jgmxnl2eqghsii6na

Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard

J Hoogeveen
1996 European Journal of Operational Research  
We show that preemptive scheduling in a two-stage flow shop with at least two identical parallel machines in one of the stages so as to minimize makespan is NP-hard in the strong sense. 1991 Mathematics  ...  McNaughton's wrap-around Nle [1959] finds a shortest preemptive schedule on identical parallel machines in Unear time.  ...  In this note. we will show that preemptive scheduling in a two-stage flow shop with at least two identical parallel machines in one of the stages so as to minimize makespan is NP-hard in the strong sense  ... 
doi:10.1016/0377-2217(94)00235-5 fatcat:2dpe64hanjgavaofqasiwjjamy

Integrality Property in Preemptive Parallel Machine Scheduling [chapter]

Philippe Baptiste, Jacques Carlier, Alexander Kononov, Maurice Queyranne, Sergey Sevastyanov, Maxim Sviridenko
2009 Lecture Notes in Computer Science  
As a straightforward consequence of this result, for a wide class of scheduling problems with unit processing times a so-called preemption redundancy property is valid.  ...  We consider parallel machine scheduling problems with identical machines and preemption allowed.  ...  Concluding Remarks In this paper we establish the integrality property for the preemptive version of the parallel machine scheduling problem with chain precedence constraints and release dates and an arbitrary  ... 
doi:10.1007/978-3-642-03351-3_6 fatcat:nutzz4wn3nbz5gunoxajxt4viy

Scheduling Jobs with Releases Dates and Delivery Times on M Identical Non-idling Machines

Fatma Hermès, Khaled Ghédira
2017 Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics  
This problem is strongly NP-hard since its particular case on only one machine has been proved to be strongly NP-hard (Chrétienne, 2008) .  ...  This paper considers the problem of scheduling jobs with release dates and delivery times on identical machines where the machines must work under the non-idling constraint.  ...  The problem , | , | is NP-hard in the strong sense since it is a generalization of the one machine scheduling problem 1, | , | which has been proved to be strongly NP-hard in (Chrétienne, 2008) .  ... 
doi:10.5220/0006428100820091 dblp:conf/icinco/HermesG17 fatcat:rmojtqhf7nbczj6t56q3sxotsy

Page 5229 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
Summary: “Preemptive scheduling in open shops and flow shops so as to minimize the mean flow time are both known to be strongly NP-hard on three or more machines.  ...  However, their complexity on two machines remained open for more than a decade. In this paper we show that open shop is NP-hard in the ordinary sense and flow shop is NP-hard in the strong sense.  ... 

Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines

Panneerselvam Senthilkumar, Sockalingam Narayanan
2010 Intelligent Information Management  
This paper presents a survey of single machine scheduling problem with uniform parallel machines.  ...  The single machine scheduling problem with uniform parallel machines consists of n jobs, each with single operation, which are to be scheduled on m parallel machines with different speeds.  ...  Meral Azizoglu and Omer Kirca [37] have considered the NP-hard problem of scheduling jobs on identical parallel machines to minimize total weighted flow time.  ... 
doi:10.4236/iim.2010.28056 fatcat:cugkndehgrgedbxdjuga7mz7e4

Notes on Max Flow Time Minimization with Controllable Processing Times

Monaldo Mastrolilli
2003 Computing  
We consider the identical parallel machines max flow time minimization problem with controllable processing times. We address the preemptive and non-preemptive version of the problem.  ...  For the non-preemptive problem it is shown that the First In First Out (FIFO) heuristic has a tight worst-case performance of 3 − 2/m, when jobs processing times and costs are set as in some optimal preemptive  ...  The Preemptive Problem The goal of this section is to find a preemptive schedule on m identical machines with minimum max flow time and total cost at most κ.  ... 
doi:10.1007/s00607-003-0029-z fatcat:y3ijy4z3ojcerf3usrmn345qku

Scheduling problems in master-slave model

Joseph Y.-T. Leung, Hairong Zhao
2007 Annals of Operations Research  
In this paper, we show that the problem of minimizing total completion time is NP-hard in the strong sense.  ...  It has been shown that the problem of minimizing makespan is NP-hard.  ...  In a preemptive schedule, a job running on one machine may be interrupted for some time, and later resumed on possibly a different machine.  ... 
doi:10.1007/s10479-007-0271-4 fatcat:smtj466k6bhkbhdy5dahhd2vwe

On scheduling malleable jobs to minimise the total weighted completion time

Ruslan Sadykov
2009 IFAC Proceedings Volumes  
In this work, we consider the NP-hard problem of scheduling malleable jobs to minimize the total weighted completion time or mean weighted flow time.  ...  This paper is about scheduling parallel jobs, i.e. which can be executed on more than one processor at the same time. Malleable jobs is a special class of parallel jobs.  ...  The problem we consider is a generalisation of the problem to schedule preemptive non-parallel jobs (δ j = 1, ∀j ∈ N ) on identical parallel machines to minimise the total weighted completion time P |  ... 
doi:10.3182/20090603-3-ru-2001.0183 fatcat:xargesjafzembnx3yarhujewqe

Hardness of Approximating Flow and Job Shop Scheduling Problems

Monaldo Mastrolilli, Ola Svensson
2011 Journal of the ACM  
The same bounds hold for the general version of flow shops, where jobs are not required to be processed on each machine.  ...  Hardness of approximating flow and job shop scheduling problems.  ...  Also, many thanks to Subhash Khot for a kind explanation of his results. M. Mastrolilli would like to dedicate this work to Edoardo on the occasion of his birth.  ... 
doi:10.1145/2027216.2027218 fatcat:ygoltztdwja5porfdynpbu5fpu

An analysis of shift class design problems

Antoon W.J. Kolen, Leo G. Kroon
1994 European Journal of Operational Research  
A number of jobs must be carried out where each job requires processing from a fixed start time to a fixed finish time.  ...  The jobs must be carried out in a non-preemptive way, although at the end of a shift preemption of a job is allowed sometimes.  ...  Y < 2Ypr ~ for the problem SCDUC. Proof. Suppose one has a preemptive schedule with Ypre machines.  ... 
doi:10.1016/0377-2217(94)90056-6 fatcat:taihls7ntnatzbjljhe7fl2dge

Page 8825 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
The paper considers the problem of scheduling a set of preemptive jobs on a set of parallel machines. For each job it must be decided whether to accept or reject.  ...  of tasks on a single machine.  ... 

Optimal Time-Critical Scheduling via Resource Augmentation

Phillips, Stein, Torng, Wein
2002 Algorithmica  
We consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments  ...  For the optimization of average flow time, these are the first results of any sort, for any MP-hard version of the problem, that indicate that it might be possible to design good approximation algorithms  ...  This Theorem 2. 1 1 SRPT i s a (2 -$)-speed algorithm for the preemptive minimization of average flow times on parallel machines.  ... 
doi:10.1007/s00453-001-0068-9 fatcat:ac35hr6ezvcctaaeo5yud35x64
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