## תקציר

The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where elements arrive one-by-one in random order, revealing a weight upon arrival. The decision whether to select an element has to be taken immediately after its arrival. The different applications that map to the secretary problem ask for different constraint families to be handled. The most prominent ones are matroid constraints, which both capture many relevant settings and admit strongly competitive secretary algorithms. However, dealing with more involved constraints proved to be much more difficult, and strong algorithms are known only for a few specific settings. In this paper, we present a general framework for dealing with the secretary problem over the intersection of several matroids. This framework allows us to combine and exploit the large set of matroid secretary algorithms known in the literature. As one consequence, we get constant-competitive secretary algorithms over the intersection of any constant number of matroids whose corresponding (single-)matroid secretary problems are currently known to have a constant-competitive algorithm. Moreover, we show that our results extend to submodular objectives.

שפה מקורית | אנגלית |
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כותר פרסום המארח | 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 |

עורכים | Artur Czumaj |

מוציא לאור | Association for Computing Machinery |

עמודים | 735-752 |

מספר עמודים | 18 |

מסת"ב (אלקטרוני) | 9781611975031 |

מזהי עצם דיגיטלי (DOIs) | |

סטטוס פרסום | פורסם - 2018 |

אירוע | 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, ארצות הברית משך הזמן: 7 ינו׳ 2018 → 10 ינו׳ 2018 |

### סדרות פרסומים

שם | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### כנס

כנס | 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 |
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מדינה/אזור | ארצות הברית |

עיר | New Orleans |

תקופה | 7/01/18 → 10/01/18 |

### הערה ביבליוגרפית

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