## Abstract

We consider the problem of assigning a set of jobs to m parallel related machines so as to maximize the minimum load over the machines. This situation corresponds to a case that a system which consists of the m machines is alive (i.e. productive) only when all machines are alive, and the system should be maintained alive as long as possible. The above problem is called related machines covering problem and is different from the related machines scheduling problem in which the goal is to minimize the maximum load. Our main result is a polynomial approximation scheme for this covering problem. To the best of our knowledge the previous best approximation algorithm has a performance ratio of 2. Also, an approximation scheme for the special case of identical machines was given by [14]. Some of our techniques are built on ideas of Hochbaum and Shmoys [12]. They provided an approximation scheme for the well known related machines scheduling. In fact, our algorithm can be adapted to provide a simpler approximation scheme for the related machines scheduling as Well.

Original language | English |
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Title of host publication | Approximation Algorithms for Combinatorial Optimization - International Workshop, APPROX 1998, Proceedings |

Editors | José Rolim, Klaus Jansen |

Publisher | Springer Verlag |

Pages | 39-47 |

Number of pages | 9 |

ISBN (Print) | 3540647368, 9783540647362 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

Event | International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 1998 - Aalborg, Denmark Duration: 18 Jul 1998 → 19 Jul 1998 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1444 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 1998 |
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Country/Territory | Denmark |

City | Aalborg |

Period | 18/07/98 → 19/07/98 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1998.

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)