### Abstract

We consider stable marriage with covering constraints (smc): in this variant of stable marriage, we distinguish a subset of women as well as a subset of men, and we seek a matching with fewest number of blocking pairs that matches all of the distinguished people. We investigate how a set of natural parameters, namely the maximum length of preference lists for men and women, the number of distinguished men and women, and the number of blocking pairs allowed determine the computational tractability of this problem.our main result is a complete complexity trichotomy that, for each choice of the studied parameters, classifies smc as polynomial-time solvable, np np\mathsf {np}-hard and fixed-parameter tractable, or np np\mathsf {np}-hard and w[1] w[1]\mathsf {w}[1]-hard. We also classify all cases of one-sided constraints where only women may be distinguished.

Original language | English |
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Title of host publication | Algorithmic Game Theory. SAGT 2017 |

Publisher | Springer |

Pages | 320-332 |

ISBN (Electronic) | 978-3-319-66700-3 |

ISBN (Print) | 978-3-319-66699-0 |

DOIs | |

Publication status | Published - 2017 |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 10504 |

## Cite this

Mnich, M., & Schlotter, I. (2017). Stable Marriage with Covering Constraints: A Complete Computational Trichotomy. In

*Algorithmic Game Theory. SAGT 2017*(pp. 320-332). Springer. Lecture Notes in Computer Science, Vol.. 10504 https://doi.org/10.1007/978-3-319-66700-3_25