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## Semi-Online Preemptive Scheduling: One Algorithm for All Variants (2008)

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Citations: | 4 - 0 self |

### Citations

512 | Bounds on multiprocessing timing anomalies. - Graham - 1969 |

376 | Bounds for certain multiprocessing anomalies. - GRAHAM - 1966 |

128 | Competitive paging with locality of reference
- Borodin, Irani, et al.
- 1995
(Show Context)
Citation Context ...icense350 T. EBENLENDR AND J. SGALL inria-00359630, version 1 - 9 Feb 2009 this type have been studied also for other online problems; the most prominent example is paging with locality of reference =-=[1]-=-. Our results We give a semi-online algorithm for preemptive scheduling on uniformly related machines which is optimal for any chosen semi-online restriction, see Section 2. This means not only the ca... |

47 |
A level algorithm for preemptive scheduling
- Horwath, Lam, et al.
- 1977
(Show Context)
Citation Context ... the machines fully, and similarly the term for k is the minimal time when the work of the k largest jobs can be completed using the k fastest machines fully. The tightness of this bound follows from =-=[10, 8, 5]-=-. Semi-online restrictions and previous work We define a general semi-online input restriction to be simply a set Ψ of allowed inputs, also called input sequences. We call a sequence a partial input i... |

36 |
An optimal algorithm for preemptive on-line scheduling
- Chen, Vliet, et al.
- 1995
(Show Context)
Citation Context ...puter-generated hard instance with no clear structure [4]. Only for identical machines, the exact ratio for any number of machines is known (i) for the online case, where it tends to e/(e − 1) ≈ 1.58 =-=[2]-=-, and (ii) for non-increasing processing times, where it tends to (1 + √ 3)/2 ≈ 1.366 [13]. We are able to prove certain relations between the approximation ratios for different restrictions. Some bas... |

30 |
Semi online algorithms for the partition problem
- Kellerer, Kotov, et al.
- 1997
(Show Context)
Citation Context ...ing the same techniques, however, some technical issues have to be handled carefully to achieve the full generality of our new result. Online preemptive scheduling was studied first in [2]. The paper =-=[12]-=- is probably the first paper which studied and compared several notions of semi-online algorithms, including known sum of processing times. Some combinationSEMI-ONLINE PREEMPTIVE SCHEDULING 353 of th... |

26 | Semi-Online Scheduling with Decreasing Job Sizes
- Seiden, Sgall, et al.
(Show Context)
Citation Context ...he exact ratio for any number of machines is known (i) for the online case, where it tends to e/(e − 1) ≈ 1.58 [2], and (ii) for non-increasing processing times, where it tends to (1 + √ 3)/2 ≈ 1.366 =-=[13]-=-. We are able to prove certain relations between the approximation ratios for different restrictions. Some basic restrictions form an inclusion chain: The inputs where the first job has the maximal si... |

23 | A lower bound for on-line scheduling on uniformly related machines
- Epstein, Sgall
- 2000
(Show Context)
Citation Context ...prove the converse: Whenever for some input J Algorithm RatioStretch with the parameter r fails, we prove that there is no r-approximation algorithm. This is based on a generalization of a lemma from =-=[7]-=- which provides the optimal lower bounds for online algorithms, as shown in [4]. The key observation in its proof is this: On an input J , if the adversary stops the input sequence at the ith job from... |

18 |
Semi on-line scheduling on two identical machines
- He, Zhang
- 1999
(Show Context)
Citation Context ...is shown that for identical machines, the approximation ratio is the same as when the jobs are non-increasing. We show that this is not the case for general speeds. This restriction was introduced in =-=[9]-=- for non-preemptive scheduling on 2 identical machines. Tightly grouped processing times. For given values ¯p and α, Ψ contains all sequences with pj ∈ [¯p,α¯p] for each j. This restriction was introd... |

17 | Preemptive scheduling of uniform processor systems
- Gonzales, Sahni
- 1978
(Show Context)
Citation Context ... the machines fully, and similarly the term for k is the minimal time when the work of the k largest jobs can be completed using the k fastest machines fully. The tightness of this bound follows from =-=[10, 8, 5]-=-. Semi-online restrictions and previous work We define a general semi-online input restriction to be simply a set Ψ of allowed inputs, also called input sequences. We call a sequence a partial input i... |

14 | Optimal preemptive semi-online scheduling to minimize makespan on two related machines
- Epstein, Favrholdt
(Show Context)
Citation Context ...ptimal approximation ratios for different semi-online restrictions and give some bounds for a large number of machines. The exact analysis of special cases for a small number of machines was given in =-=[6, 3, 11]-=- for various restrictions, and in many more cases for non-preemptive scheduling. Typically, these results involve similar but ad hoc algorithms and an extensive case analysis which is tedious to verif... |

12 | Optimal and online preemptive scheduling on uniformly related machines - Ebenlendr, Sgall |

11 | Preemptive Online Scheduling: Optimal Algorithms for All Speeds
- Ebenlendr, Jawor, et al.
- 2006
(Show Context)
Citation Context ...pears to be much harder, and even in the online case we only know that the ratio is between 2.054 and e ≈ 2.718; the lower bound is shown by a computer-generated hard instance with no clear structure =-=[4]-=-. Only for identical machines, the exact ratio for any number of machines is known (i) for the online case, where it tends to e/(e − 1) ≈ 1.58 [2], and (ii) for non-increasing processing times, where ... |

10 |
Semi-online problems on two identical machines with combined partial information
- Tan, He
(Show Context)
Citation Context ...ed and compared several notions of semi-online algorithms, including known sum of processing times. Some combinationSEMI-ONLINE PREEMPTIVE SCHEDULING 353 of the previous restrictions were studied in =-=[14]-=- for non-preemptive scheduling on identical machines. We should note that there are also semi-online models that do not fit into our framework at all. For example, the algorithm may get a hint which j... |

6 |
Optimal Preemptive Semi-Online Scheduling on Two Uniform
- Du
(Show Context)
Citation Context ...ptimal approximation ratios for different semi-online restrictions and give some bounds for a large number of machines. The exact analysis of special cases for a small number of machines was given in =-=[6, 3, 11]-=- for various restrictions, and in many more cases for non-preemptive scheduling. Typically, these results involve similar but ad hoc algorithms and an extensive case analysis which is tedious to verif... |

4 | Optimal semi-online algorithms for preemptive scheduling problems with inexact partial information
- Jiang, He
(Show Context)
Citation Context ...ptimal approximation ratios for different semi-online restrictions and give some bounds for a large number of machines. The exact analysis of special cases for a small number of machines was given in =-=[6, 3, 11]-=- for various restrictions, and in many more cases for non-preemptive scheduling. Typically, these results involve similar but ad hoc algorithms and an extensive case analysis which is tedious to verif... |

4 |
Semi-online scheduling problems on two identical machines with inexact partial information
- Tan, He
(Show Context)
Citation Context ...n this case, some of the previously considered values (optimal makespan, sum of job sizes, maximal job size) is not known exactly but only up to a certain factor. These variants were studied first in =-=[15]-=- without preemption and then in [11] for preemptive scheduling; both on identical machines. Online scheduling. Here Ψ contains all sequences. In our (i.e., the authors and Wojtek Jawor) previous work ... |

3 | Semi-online scheduling jobs with tightly-grouped processing times on three identical machines - He, Dosa - 2005 |

2 | Semi-online problems on identical machines with inexact partial information - Tan, He - 2005 |