### Abstract

Linear cartograms visualize travel times between locations, usually by deforming the underlying map such that Euclidean distance corresponds to travel time. We introduce an alternative model, where the map and the locations remain fixed, but edges are drawn as sinusoid curves. Now the travel time over a road corresponds to the length of the curve. Of course the curves might intersect if not placed carefully. We study the corresponding algorithmic problem and show that suitable placements can be computed efficiently. However, the problem of placing as many curves as possible in an ideal, centered position is NP-hard. We introduce three heuristics to optimize the number of centered curves and show how to create animated visualizations.

Original language | English |
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Title of host publication | Proc. of the 8th International Conference on Geographic Information Science (GIScience) |

Editors | M. Duckham, E. Pebesma, K. Stewart, A.U. Frank |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 18-33 |

ISBN (Print) | 978-3-319-11592-4 |

DOIs | |

Publication status | Published - 2014 |

Event | conference; Eighth International Conference on Geographic Information Science - Vienna, Austria Duration: 24 Sep 2014 → 26 Sep 2014 |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 8728 |

ISSN (Print) | 0302-9743 |

### Conference

Conference | conference; Eighth International Conference on Geographic Information Science |
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Abbreviated title | GIScience' 14 |

Country | Austria |

City | Vienna |

Period | 24/09/14 → 26/09/14 |

Other | 8th International Conference, GIScience' 14, Vienna, Austria, September 24-26, 2014. |

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## Cite this

Buchin, K., van Goethem, A. I., Hoffmann, M., van Kreveld, M. J., & Speckmann, B. (2014). Travel-time maps : linear cartograms with fixed vertex locations. In M. Duckham, E. Pebesma, K. Stewart, & A. U. Frank (Eds.),

*Proc. of the 8th International Conference on Geographic Information Science (GIScience)*(pp. 18-33). (Lecture Notes in Computer Science; Vol. 8728). Springer. https://doi.org/10.1007/978-3-319-11593-1_2