## Abstract

We consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of n items, where each item can be selected in one of several D-dimensional incarnations. We are also given T bin types, each with its own cost and D-dimensional size. Our goal is to pack the items in a set of bins of minimum overall cost. The problem is motivated by scheduling in networks with guaranteed quality of service (QoS), but due to its general formulation it has many other applications as well. We present an approximation algorithm that is guaranteed to produce a solution whose cost is about ln D times the optimum. For the running time to be polynomial we require D = O(1) and T = O(log n). This extends previous results for vector bin packing, in which each item has a single incarnation and there is only one bin type. To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack a maximum weight set of (incarnations of) items in that bin.

Original language | English |
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Title of host publication | Algorithm Theory - SWAT 2010 - 12th Scandinavian Symposium and Workshops on Algorithm Theory, Proceedings |

Pages | 248-259 |

Number of pages | 12 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

Event | 12th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2010 - Bergen, Norway Duration: 21 Jun 2010 → 23 Jun 2010 |

### 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 | 6139 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 12th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2010 |
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Country/Territory | Norway |

City | Bergen |

Period | 21/06/10 → 23/06/10 |

### Bibliographical note

Funding Information:The work of Boaz Patt-Shamir was supported in part by the Israel Science Foundation (grant 1372/09 ) and by Israel Ministry of Science and Technology .