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Competitive-Ratio Approximation Schemes for Minimizing the Makespan in the Online-List Model [article]

Nicole Megow, Andreas Wiese
2013 arXiv   pre-print
For any number of identical parallel or uniformly related machines, we provide a competitive-ratio approximation scheme that computes an online algorithm whose competitive ratio is arbitrarily close to  ...  We consider online scheduling on multiple machines for jobs arriving one-by-one with the objective of minimizing the makespan.  ...  The current research on competitive-ratio approximation schemes focussed on particular online scheduling problems.  ... 
arXiv:1303.1912v1 fatcat:sjfvbohdj5fmpg4kgy57kkwtam

A General Scheme for Designing Monotone Algorithms for Scheduling Problems with Precedence Constraints [chapter]

Clemens Thielen, Sven O. Krumke
2009 Lecture Notes in Computer Science  
a monotone approximation/ competitive algorithm for the problem on related machines.  ...  It takes as input two approximation/competitive algorithms for the (simpler) scheduling problems P |prec, rj|γ on identical machines and 1|prec, rj|γ on a single machine and then generically constructs  ...  The General Scheme We now present our general scheme for constructing a monotone approximation/competitive algorithm for a problem Π ∈ C from given approximation/ competitive algorithms A id for Π id and  ... 
doi:10.1007/978-3-540-93980-1_9 fatcat:3vbuc4x7z5bpnf6q6g6m6dpvly

Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines

Panneerselvam Senthilkumar, Sockalingam Narayanan
2010 Intelligent Information Management  
Since, this scheduling problem is a combinatorial problem; usage of a heuristic is inevitable to obtain solution in polynomial time.  ...  This paper presents a survey of single machine scheduling problem with uniform parallel machines.  ...  They provided an approximation scheme for the related machines scheduling. Their algorithm can be adapted to provide a simpler approximation scheme for the related machines scheduling too.  ... 
doi:10.4236/iim.2010.28056 fatcat:cugkndehgrgedbxdjuga7mz7e4

Online Scheduling with Bounded Migration [chapter]

Peter Sanders, Naveen Sivadasan, Martin Skutella
2004 Lecture Notes in Computer Science  
We also present a linear time 'online approximation scheme', that is, a family of online algorithms with competitive ratio 1 + and constant migration factor β( ), for any fixed > 0.  ...  For small values of β, we obtain several simple online algorithms with constant competitive ratio.  ...  We would also like to thank Gerhard Woeginger for interesting discussions and helpful comments on the topic of this paper.  ... 
doi:10.1007/978-3-540-27836-8_92 fatcat:llzrystvnzc4ln6plpttf66etq

Multiprocessor Scheduling with Rejection

Yair Bartal, Stefano Leonardi, Alberto Marchetti-Spaccamela, Jirí Sgall, Leen Stougie
2000 SIAM Journal on Discrete Mathematics  
For the off-line problem we present a fully polynomial approximation scheme for fixed m and a polynomial approximation scheme for arbitrary m.  ...  The main result is a 1 + φ ≈ 2.618 competitive algorithm for the on-line version of the problem, where φ is the golden ratio.  ...  We thank Giorgio Gallo for having drawn our attention to this scheduling problem. We thank the anonymous referees for numerous helpful comments.  ... 
doi:10.1137/s0895480196300522 fatcat:olpoaiah4vb7fbopqleifmwzoa

Online Scheduling with Bounded Migration

Peter Sanders, Naveen Sivadasan, Martin Skutella
2009 Mathematics of Operations Research  
We also present a linear time 'online approximation scheme', that is, a family of online algorithms with competitive ratio 1 + and constant migration factor β( ), for any fixed > 0.  ...  For small values of β, we obtain several simple online algorithms with constant competitive ratio.  ...  We would also like to thank Gerhard Woeginger for interesting discussions and helpful comments on the topic of this paper.  ... 
doi:10.1287/moor.1090.0381 fatcat:4rdzvj2jjnht3foeesyuxz2s2m

Scheduling with step-improving processing times

T.C. Edwin Cheng, Yong He, Han Hoogeveen, Min Ji, Gerhard J. Woeginger
2006 Operations Research Letters  
For this problem we give an NP-hardness proof, a fast pseudo-polynomial time algorithm, an FPTAS, and an on-line algorithm with best possible competitive ratio.  ...  We consider the scheduling problem of minimizing the makespan on a single machine with step-improving job processing times around a common critical date.  ...  Han Hoogeveen and Gerhard Woeginger are grateful to the organizers of the workshop and to the staff of Dagstuhl for providing a stimulating atmosphere. T  ... 
doi:10.1016/j.orl.2005.03.002 fatcat:4nh6guolu5hv7ocvm4uyazjvni

Single-machine scheduling under the job rejection constraint

Liqi Zhang, Lingfa Lu, Jinjiang Yuan
2010 Theoretical Computer Science  
In addition, we provide a fully polynomial-time approximation scheme for the makespan problem with release dates.  ...  For other objective functions related to due dates, we point out that there is no approximation algorithm with a bounded approximation ratio.  ...  For the on-line version, they present a best-possible on-line algorithm with a competitive ratio √ 5+3 2 ≈ 2.618; for the off-line version, they present a polynomial-time approximation scheme.  ... 
doi:10.1016/j.tcs.2010.02.006 fatcat:2l2py4zpvzg6zpmry3nv6rxtty

Improved Rejection Penalty Algorithm with Multiprocessor Rejection Technique

Prativa Satpathy, Kalyan Das, Jagamohan Padhi
2015 International Journal of Electrical and Computer Engineering (IJECE)  
Our proposed 'Improved Reject penalty algorithm' reduce competitive ratio, which in turn enhances the efficiency of the on-line algorithm.  ...  Our objective is to minimize the makespan of the scheduled job and to minimize the sum of the penalties of rejected jobs.  ...  RESEARCH METHOD In the existing RP() algorithm, there is an open problem area for improving the () value so that makespan is minimized, resulting in the automatic reduction of the competitive ratio as  ... 
doi:10.11591/ijece.v5i3.pp477-482 fatcat:ht3az2gnyre6vkiu6xyvwhoujq

Scheduling of Independent Dedicated Multiprocessor Tasks [chapter]

Evripidis Bampis, Massimiliano Caramia, Jiří Fiala, Aleksei V. Fishkin, Antonio Iovanella
2002 Lecture Notes in Computer Science  
We analyze the algorithm for both tasks arrive over time and tasks arrive over list on-line scheduling versions, and show that its competitive ratio is bounded by 2 √ m and 2 √ m + 1, respectively.  ...  Then, by using our split-round technique, we give a 3 √ m-approximation algorithm for the off-line version of the problem.  ...  We thank to Maxim Sviridenko for giving us useful comments and ideas.  ... 
doi:10.1007/3-540-36136-7_35 fatcat:mo42clnlibd3tpnx7t2mebkld4

A New Approach to Online Scheduling: Approximating the Optimal Competitive Ratio [article]

Elisabeth Günther, Olaf Maurer, Nicole Megow, Andreas Wiese
2012 arXiv   pre-print
We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes.  ...  Such a scheme algorithmically constructs an online algorithm with a competitive ratio arbitrarily close to the best possible competitive ratio for any online algorithm.  ...  E Competitive-Ratio Approximation Schemes for Minimizing C max (cf. Section 6) Consider the objective of minimizing the makespan.  ... 
arXiv:1204.0897v2 fatcat:xvnafqol2zeltdipdzuytq6zf4

A New Approach to Online Scheduling: Approximating the Optimal Competitive Ratio [chapter]

Elisabeth Günther, Olaf Maurer, Nicole Megow, Andreas Wiese
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitiveratio approximation schemes.  ...  Such a scheme algorithmically constructs an online algorithm with a competitive ratio arbitrarily close to the best possible competitive ratio for any online algorithm.  ...  In this paper, we introduce the concept of competitive-ratio approximation schemes and present such schemes for various scheduling problems with jobs arriving online over time.  ... 
doi:10.1137/1.9781611973105.9 dblp:conf/soda/GuntherMMW13 fatcat:n2qhvxso6rd4xmj5m4sqmc7jei

Page 6953 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
For this strongly NP-hard problem, a linear-time approximation scheme is derived which gives for any fixed ¢ > 0 a feasible schedule with a makespan at most (1 +e) times the optimum.  ...  [Jansen, Klaus] (D-KIEL-I; Kiel) ; Porkolab, L. (4-LNDIC-C; London) Linear-time approximation schemes for scheduling malleable parallel tasks.  ... 

Online malleable job scheduling for

Jessen T. Havill
2010 Information Processing Letters  
We also provide a similar online algorithm for the more general problem with job dependent overhead term c j that has optimal competitive ratio φ = (1+ √ 5)/2.  ...  We provide online algorithms for m = 2 and m = 3 with asymptotically optimal competitive ratios of 3/2 and 5/3, respectively.  ...  There have also been a number of papers that study approximation algorithms and polynomial time approximation schemes for variants of the offline malleable job scheduling problem; for some of the more  ... 
doi:10.1016/j.ipl.2010.10.010 fatcat:abvmpsbu6refnaxp7rw3fb3fiy

Scheduling parallel jobs to minimize the makespan

Berit Johannes
2006 Journal of Scheduling  
This gives the best-known approximation algorithms for both the preemptive and the nonpreemptive variant of the problem.  ...  Still, we present the first online algorithm for scheduling parallel jobs with a constant competitive ratio in this context.  ...  Acknowledgments I am grateful to Martin Skutella for directing me to this research area. I also thank him and Rolf Möhring for various helpful comments.  ... 
doi:10.1007/s10951-006-8497-6 fatcat:xs2h2c6gsvfixjmr2yw3eg556q
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