## Abstract

Given a set of jobs, each consisting of a number of weighted intervals on the real line, and a number m of machines, we study the problem of selecting a maximum weight subset of the intervals such that at most one interval is selected from each job and, for any point p on the real line, at most m intervals containing p are selected. This problem has applications in molecular biology, caching, PCB assembly, and scheduling. We give a parameterized algorithm GREEDY_{α} and show that there are values of the parameter α so that GREEDY_{α} produces a ½ -approximation in the case of unit weights, a ⅛ -approximation in the case of arbitrary weights, and a (3 − 2 √2)-approximation in the case where the weights of all intervals corresponding to the same job are equal. Algorithm GREEDY_{α} belongs to the class of “myopic” algorithms, which are deterministic algorithms that process the given intervals in order of non-decreasing right endpoints and can either reject or select each interval (rejections are irrevocable).We use competitive analysis to show that GREEDY_{α} is an optimal myopic algorithm in the case of unit weights and in the case of equal weights per job, and is close to optimal in the case of arbitrary weights.

Original language | English |
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Title of host publication | Algorithms and Computation - 11th International Conference, ISAAC 2000, Proceedings |

Editors | G. Goos, J. Hartmanis, J. van Leeuwen, D.T. Lee, S.H. Teng |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 228-240 |

Number of pages | 13 |

ISBN (Electronic) | 978-3-540-40996-0 |

ISBN (Print) | 978-3-540-41255-7 |

DOIs | |

Publication status | Published - 2000 |

Externally published | Yes |

Event | 11th Annual International Symposium on Algorithms and Computation, (ISAAC 2000) - Taipei, Taiwan Duration: 18 Dec 2000 → 20 Dec 2000 Conference number: 11 |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 1969 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 11th Annual International Symposium on Algorithms and Computation, (ISAAC 2000) |
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Abbreviated title | ISAAC 2000 |

Country/Territory | Taiwan |

City | Taipei |

Period | 18/12/00 → 20/12/00 |