### Abstract

In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time. We therefore focus on similarity measures for surfaces, specifically the Fréchet distance between surfaces. While the Fréchet distance between surfaces is not even known to be computable, we show for variants arising in the context of moving curves that they are polynomial-time solvable or NP-complete depending on the restrictions imposed on how the moving curves are matched. We achieve the polynomial-time solutions by a novel approach for computing a surface in the so-called free-space diagram based on max-flow min-cut duality.

Original language | English |
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Title of host publication | Proc. 23rd Annual European Symposium on Algorithms (ESA) |

Editors | N. Bansal, I. Finocchi |

Publisher | Springer |

Pages | 928-940 |

ISBN (Print) | 978-3-662-48349-7 |

DOIs | |

Publication status | Published - 2015 |

Event | 23rd Annual European Symposium on Algorithms (ESA 2015) - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015 Conference number: 23 http://algo2015.upatras.gr/esa/ |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 9294 |

ISSN (Print) | 0302-9743 |

### Conference

Conference | 23rd Annual European Symposium on Algorithms (ESA 2015) |
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Abbreviated title | ESA 2015 |

Country | Greece |

City | Patras |

Period | 14/09/15 → 16/09/15 |

Internet address |

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## Cite this

Buchin, K., Ophelders, T. A. E., & Speckmann, B. (2015). Computing the similarity between moving curves. In N. Bansal, & I. Finocchi (Eds.),

*Proc. 23rd Annual European Symposium on Algorithms (ESA)*(pp. 928-940). (Lecture Notes in Computer Science; Vol. 9294). Springer. https://doi.org/10.1007/978-3-662-48350-3_77