### Abstract

We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of 2 and min{m-k+1,O(√k)} respectively, matching the approximation ratios of best known polynomial-time algorithms (for max-min fairness, the latter claim is true for certain ratios of the number of goods m to people k). Our mechanisms are obtained by establishing a polynomial-time approximation-sensitive reduction from the problem of designing approximately optimal mechanisms for some arbitrary objective O to that of designing bi-criterion approximation algorithms for the same objective O plus a linear allocation cost term. Our reduction is itself enabled by extending the celebrated "equivalence of separation and optimization" [27, 32] to also accommodate bi-criterion approximations. Moreover, to apply the reduction to the specific problems of makespan and max-min fairness we develop polynomial-time bi-criterion approximation algorithms for makespan minimization with costs and max-min fairness with costs, adapting the algorithms of [45], [10] and [4] to the type of bi-criterion approximation that is required by the reduction.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 |

Publisher | Association for Computing Machinery |

Pages | 1934-1952 |

Number of pages | 19 |

Edition | January |

ISBN (Electronic) | 9781611973747 |

DOIs | |

State | Published - Jan 1 2015 |

Externally published | Yes |

Event | 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 - San Diego, United States Duration: Jan 4 2015 → Jan 6 2015 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
---|---|

Number | January |

Volume | 2015-January |

### Other

Other | 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 |
---|---|

Country | United States |

City | San Diego |

Period | 1/4/15 → 1/6/15 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

## Fingerprint Dive into the research topics of 'Bayesian truthful mechanisms for job scheduling from bi-criterion approximation algorithms'. Together they form a unique fingerprint.

## Cite this

*Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015*(January ed., pp. 1934-1952). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2015-January, No. January). Association for Computing Machinery. https://doi.org/10.1137/1.9781611973730.130