### Volume 8

n° 1 (2006), pp. 1-16author: | Angelelli, Enrico, Speranza, Maria Grazia, and Tuza, Tsolt |
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title: | New bounds and algorithms for on-line scheduling: two identical processors, known sum and upper bound on the tasks |

keywords: | semi on-line scheduling, parallel processors, competitive analysis |

abstract: | In this paper we study a semi on-line version of the classical multiprocessor scheduling problem on two identical processors. We assume that the sum of the tasks and an upper bound gamma on the size of each task are known. Each task has to be assigned upon arrival and the assignment cannot be changed later. The objective is the minimization of the maximum completion time on the processors. In this paper we propose new algorithms and improve known lower and upper bounds on the competitive ratio. Algorithms and bounds depend on the value of gamma. An optimal algorithm is obtained for gamma in the interval [ 1/n,2(n+1)/n(2n+1) ] and gamma = (2n-1)/2n(n-1), where n is any integer value larger or equal 2. |

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reference: | Angelelli, Enrico and Speranza, Maria Grazia, and Tuza, Tsolt (2006),
New bounds and algorithms for on-line scheduling: two identical processors, known sum and upper bound on the tasks,
Discrete Mathematics and Theoretical Computer Science 8, pp. 1-16 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Mon Jan 30 21:52:29 CET 2006 by falk