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Generalizing the Kawaguchi-Kyan bound to stochastic parallel machine scheduling [article]

Sven Jäger, Martin Skutella
2018 arXiv   pre-print
For the special case of deterministic scheduling (i.e., $\Delta=0$), our bound matches the tight performance ratio $\frac12(1+\sqrt{2})$ of this algorithm (WSPT rule), derived by Kawaguchi and Kyan in  ...  Minimizing the sum of weighted completion times on $m$ identical parallel machines is one of the most important and classical scheduling problems.  ...  In return, the generalized Kawaguchi-Kyan bound is better for these α.  ... 
arXiv:1801.01105v1 fatcat:ixb4aummhvgzravh5un3pyhb2u

Generalizing the Kawaguchi-Kyan Bound to Stochastic Parallel Machine Scheduling

Sven Jäger, Martin Skutella
unpublished
For the special case of deterministic scheduling (i.e., ∆ = 0), our bound matches the tight performance ratio 1 2 (1+ √ 2) of this algorithm (WSPT rule), derived by Kawaguchi and Kyan in a 1986 landmark  ...  Minimizing the sum of weighted completion times on m identical parallel machines is one of the most important and classical scheduling problems.  ...  Kawaguchi-Kyan Bound to Stochastic Parallel Machine Scheduling optimal schedule for the auxiliary problem to the expected objective value of the schedule obtained by an optimal policy for the original  ... 
fatcat:edek5td5xnh3bk5auiz7vtolxa

Lower Bounds for Smith's Rule in Stochastic Machine Scheduling [chapter]

Caroline Jagtenberg, Uwe Schwiegelshohn, Marc Uetz
2011 Lecture Notes in Computer Science  
We consider the problem to minimize the weighted sum of completion times in nonpreemptive parallel machine scheduling.  ...  In a landmark paper from 1986, Kawaguchi and Kyan [5] showed that scheduling the jobs according to the WSPT rule -also known as Smith's rulehas a performance guarantee of 1 2 (1 + √ 2) ≈ 1.207.  ...  Acknowledgements The second and third author thank the organizers of the 2010 Dagstuhl Seminar on Scheduling.  ... 
doi:10.1007/978-3-642-18318-8_13 fatcat:gomsy5gobzcmrlmpyqp2powane

Analysis of Smith's rule in stochastic machine scheduling

Caroline Jagtenberg, Uwe Schwiegelshohn, Marc Uetz
2013 Operations Research Letters  
≈ 1.207 for minimizing the weighted sum of completion times in parallel machine scheduling.  ...  In a landmark paper from 1986, Kawaguchi and Kyan show that scheduling jobs according to ratios weight over processing time -also known as Smith's rule-has a tight performance guarantee of (1 + √ 2)/2  ...  The second and third author thank the organizers of the 2010 Dagstuhl Seminar on Scheduling, which was a starting point for this work. We also thank an anonymous referee for helpful comments.  ... 
doi:10.1016/j.orl.2013.08.001 fatcat:5fvxjbizjbbqdjl5geo7lxcqr4

Scheduling (Dagstuhl Seminar 18101)

Magnús M. Halldórson, Nicole Megow, Clifford Stein, Michael Wagner
2018 Dagstuhl Reports  
The primary objective of the seminar was to expose each community to the important problems and techniques from the other community, and to facilitate dialog and collaboration between researchers.  ...  This report documents the program and outcomes of the Dagstuhl Seminar 18101 "Scheduling" in March 2018.  ...  URL http://dx.doi.org/10.1137/1.9781611975031.52 Kawaguchi-Kyan Bound to Stochastic Parallel Machine Scheduling Sven Jäger, Martin Skutella Main reference Sven Jäger, Martin Skutella: "Generalizing the  ... 
doi:10.4230/dagrep.8.3.1 dblp:journals/dagstuhl-reports/HalldorssonMS18 fatcat:xlfjfzwt3fdpdk3ryxr2ldra5m

Scheduling (Dagstuhl Seminar 13111)

Susanne Albers, Onno J. Boxma, Kirk Pruhs, Marc Herbstritt
2013 Dagstuhl Reports  
The primary objective of the seminar is to facilitate dialog and collaboration between researchers in two different mathematically-oriented scheduling research communities, the stochastic scheduling and  ...  This report documents the program and the outcomes of Dagstuhl Seminar 13111 "Scheduling".  ...  The open problem is to find the true performance bound for Smith's rule in stochastic parallel machine scheduling.  ... 
doi:10.4230/dagrep.3.3.24 dblp:journals/dagstuhl-reports/AlbersBP13 fatcat:f3jsoas3o5ewdl2wuvwz7kfpte

The Expected Competitive Ratio for Weighted Completion Time Scheduling [chapter]

Alexander Souza, Angelika Steger
2004 Lecture Notes in Computer Science  
A set of n independent jobs is to be scheduled without preemption on m identical parallel machines.  ...  We show a general bound on the expected competitive ratio for list scheduling algorithms, which holds for a class of so-called new-better-than-used processing time distributions.  ...  Acknowledgement The authors thank the anonymous referees for references and suggestions which helped improve the paper.  ... 
doi:10.1007/978-3-540-24749-4_54 fatcat:q4gursidrzhehm3662tuyzs3em

The Expected Competitive Ratio for Weighted Completion Time Scheduling

Alexander Souza, Angelika Steger
2005 Theory of Computing Systems  
A set of n independent jobs is to be scheduled without preemption on m identical parallel machines.  ...  We show a general bound on the expected competitive ratio for list scheduling algorithms, which holds for a class of so-called new-better-than-used processing time distributions.  ...  Acknowledgement The authors thank the anonymous referees for references and suggestions which helped improve the paper.  ... 
doi:10.1007/s00224-005-1261-z fatcat:7g4l2tmucfexfbelkkrodlgk64

Fixed-Order Scheduling on Parallel Machines [chapter]

Thomas Bosman, Dario Frascaria, Neil Olver, René Sitters, Leen Stougie
2019 Lecture Notes in Computer Science  
We consider the following natural scheduling problem: Given a sequence of jobs with weights and processing times, one needs to assign each job to one of m identical machines in order to minimize the sum  ...  The twist is that for machine the jobs assigned to it must obey the order of the input sequence, as is the case in multi-server queuing systems.  ...  The Kawaguchi-Kyan bound of 1+ √ 2 2 ≈ 1.207 is known to be tight [11, 17] , and this lower bound carries over to fixed-order scheduling: the worst-case example uses jobs with equal Smith ratios, and  ... 
doi:10.1007/978-3-030-17953-3_7 fatcat:ga5yirjqvbh5hav7kwdrysvdxe

Elements of Scheduling [article]

Jan Karel Lenstra, David B. Shmoys
2020 arXiv   pre-print
It was a natural idea to turn the theses into a textbook on scheduling.  ...  We continue to receive requests from colleagues who look for a text on the elements of scheduling at an advanced undergraduate or early graduate level.  ...  and flow shop scheduling by Kawaguchi and Kyan [1988] .  ... 
arXiv:2001.06005v1 fatcat:5w7dwzh6nrbb7ateihvrac3734

Page 1087 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
A perspective on queueing models of computer performance. 89j:68017 Lehtonen, Tapani Scheduling jobs with exponential processing times on parallel machines. 89j:68018 Litvinenko, A.  ...  (with Rosberg, Zvi) Maximal throughput in a tandem multi-hop radio network. 89k:68007 Kawaguchi, Tsuyoshi (with Kyan, Seiki) Deterministic scheduling in computer systems: a survey.  ... 

Approximation in deterministic and stochastic machine scheduling [article]

Sven Joachim Jäger, Technische Universität Berlin, Martin Skutella
2021
In the considered problems the task is to create a schedule for the processing of a set of jobs on machines running in parallel. The jobs have different processing times and priorities.  ...  In stochastic scheduling we are interested in upper bounds for the ratio of the expected objective value resulting from the considered policy to the expected objective value under an optimal policy.  ...  We generalize the bound by Kawaguchi and Kyan [KK86] and its refinements from Chapter 3 to stochastic scheduling.  ... 
doi:10.14279/depositonce-12198 fatcat:27vjkoxhq5gbnjukkl4aitbtqu

A Framework for Scheduling with Online Availability [chapter]

Florian Diedrich, Ulrich M. Schwarz
Lecture Notes in Computer Science  
With the increasing popularity of large-scale distributed computing networks, a new aspect has to be considered for scheduling problems: machines may not be available permanently, but may be withdrawn  ...  We give several results for completion time based objectives: 1. we show that scheduling independent jobs on identical machines with online failures to minimize the sum of completion times is (8/7 − )-  ...  Conclusion In this paper we have presented a simple yet general framework permitting the transfer of results from offline scheduling settings to natural preemptive online extensions.  ... 
doi:10.1007/978-3-540-74466-5_23 fatcat:ucqqax3g4zel3bmv6psxpv6nhq

New utilization criteria for online scheduling

Mohamed Hussein, Technische Universität Dortmund, Technische Universität Dortmund
2005
This thesis deals with the problem of non-preemptive scheduling independent jobs on m identical parallel machines. In our online model, the jobs are submitted over time non-clairvoyantly.  ...  Our main scheduling objective is to maximize the utilization of the system.  ...  Their result improves upon the previous best known bound by KAWAGUCHI and KYAN [44] .  ... 
doi:10.17877/de290r-12516 fatcat:nebu3eok6nbbfgqwhvqnhqqfki

Computational Geometry (Dagstuhl Seminar 13101) Scheduling (Dagstuhl Seminar 13111) Future Internet (Dagstuhl Seminar 13131)

Otfried Cheong, Kurt Mehlhorn, Monique, Susanne Albers, Onno Boxma, Kirk, Erik Demaine, Fedor Fomin, Mohammadtaghi Hajiaghayi, Dimitrios, Jon Crowcroft, Markus Fidler (+2 others)
2013 unpublished
The open problem is to find the true performance bound for Smith's rule in stochastic parallel machine scheduling.  ...  a landmark paper from 1986, Kawaguchi and Kyan show that scheduling jobs according to ratios weight over processing time -a.k.a.  ...  One of the biggest challenges related to the Future Internet in general and Software-Defined Networking (SDN) more specifically, is that the current Internet architecture is ossified, i.e. it can hardly  ... 
fatcat:6benpx4q2rfbzjefimwstubfoe
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