### Abstract

We initiate the systematic algorithmic study for gerrymandering over graphs that was recently introduced by Cohen-Zemach, Lewen-berg and Rosenschein. Namely, we study a strategic procedure for a political districting designer to draw electoral district boundaries so that a particular target candidate can win in an election. We focus on the existence of such a strategy under the plurality voting rule, and give interesting contrasts which classify easy and hard instances with respect to polynomial-time solvability. For example, we prove that the problem for trees is strongly NP-complete (thus unlikely to have a pseudo-polynomial-time algorithm), but has a pseudo-polynomial-time algorithm when the number of candidates is constant. Another example is to prove that the problem for complete graphs is NP-complete when the number of electoral districts is two, while is solvable in polynomial time when it is more than two.

Original language | English |
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Title of host publication | 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019 |

Publisher | International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS) |

Pages | 1413-1421 |

Number of pages | 9 |

ISBN (Electronic) | 9781510892002 |

Publication status | Published - Jan 1 2019 |

Event | 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019 - Montreal, Canada Duration: May 13 2019 → May 17 2019 |

### Publication series

Name | Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS |
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Volume | 3 |

ISSN (Print) | 1548-8403 |

ISSN (Electronic) | 1558-2914 |

### Conference

Conference | 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019 |
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Country | Canada |

City | Montreal |

Period | 5/13/19 → 5/17/19 |

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Software
- Control and Systems Engineering

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## Cite this

*18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019*(pp. 1413-1421). (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS; Vol. 3). International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).