### Abstract

A geographic network is a graph whose vertices are restricted to lie in a prescribed region in the plane. In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic network be drawn without crossings? We focus on the seemingly simple setting where each region is a unit length vertical segment, and one wants to connect pairs of segments with a path that lies inside the convex hull of the two segments. We prove that when paths must be drawn as straight line segments, it is NP-complete to determine if a crossing-free solution exists. In contrast, we show that when paths must be monotone curves, the question can be answered in polynomial time. In the more general case of paths that can have any shape, we show that the problem is polynomial under certain assumptions.

Original language | English |
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Title of host publication | Graph drawing and network visualization - 25th International Symposium, GD 2017, Revised Selected Papers |

Editors | F. Frati, K.-L. Ma |

Place of Publication | Cham |

Publisher | Springer |

Pages | 454-461 |

Number of pages | 8 |

ISBN (Electronic) | 978-3-319-73915-1 |

ISBN (Print) | 978-3-319-73914-4 |

DOIs | |

Publication status | Published - 2018 |

Event | 25th International Symposium on Graph Drawing and Network Visualization (GD 2017) - Boston, United States Duration: 25 Sep 2017 → 27 Sep 2017 Conference number: 25 https://gd2017.ccis.northeastern.edu/ |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 10692 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 25th International Symposium on Graph Drawing and Network Visualization (GD 2017) |
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Abbreviated title | GD 2017 |

Country | United States |

City | Boston |

Period | 25/09/17 → 27/09/17 |

Internet address |

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## Cite this

*Graph drawing and network visualization - 25th International Symposium, GD 2017, Revised Selected Papers*(pp. 454-461). (Lecture Notes in Computer Science ; Vol. 10692). Springer. https://doi.org/10.1007/978-3-319-73915-1_35