## Abstract

Scheduling dependent jobs on multiple machines is modeled as a graph (multi)coloring problem. The focus of this work is on the sum of completion times measure. This is known as the sum (multi)coloring of the conflict graph. We also initiate the study of the waiting time and the robust throughput of colorings. For uniform-length tasks we give an algorithm which simultaneously approximates these two measures, as well as sum coloring and the chromatic number, within constant factor, for any graph in which the k-colorable subgraph problem is polynomially solvable. In particular, this improves the best approximation ratio known for sum coloring interval graphs from 2 to 1.665. We then consider the problem of scheduling non-preemptively tasks (of non-uniform lengths) that require exclusive use of dedicated processors. The objective is to minimize the sum of completion times. We obtain the first constant factor approximations for this problem, when each task uses a constant number of processors.

Original language | English |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization |

Subtitle of host publication | Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings |

Editors | Luca Trevisan, Klaus Jansen, Michel Goemans, Jose D. P. Rolim |

Publisher | Springer Verlag |

Pages | 114-126 |

Number of pages | 13 |

ISBN (Electronic) | 3540424709 |

State | Published - 2015 |

Event | 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001 - Berkeley, United States Duration: 18 Aug 2001 → 20 Aug 2001 |

### 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 | 2129 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001 |
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Country/Territory | United States |

City | Berkeley |

Period | 18/08/01 → 20/08/01 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2001