### Abstract

All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; then they use this oracle to find the optimum among a finite set of critical values. We present a novel approach that avoids the detour through the decision version. We demonstrate its strength by presenting a quadratic time algorithm for the Fréchet distance between polygonal curves in R^d under polyhedral distance functions, including L_1 and L_infinity. We also get a (1+eps)-approximation of the Fréchet distance under the Euclidean metric. For the exact Euclidean case, our framework currently gives an algorithm with running time O(n^2 log^2 n). However, we conjecture that it may eventually lead to a faster exact algorithm.

Original language | English |
---|---|

Title of host publication | 21st Annual European Symposium on Algorithms (ESA) |

Editors | H.L. Bodlaender, G.F. Italiano |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 241-252 |

ISBN (Print) | 978-3-642-40449-8 |

DOIs | |

Publication status | Published - 2013 |

Event | 21st Annual European Symposium on Algorithms (ESA 2013) - Sophia Antipolis, France Duration: 2 Sep 2013 → 4 Sep 2013 Conference number: 21st http://www.informatik.uni-trier.de/~ley/db/conf/esa/esa2013.html |

### Publication series

Name | Lecture Notes in Computer Science |
---|---|

Volume | 8125 |

ISSN (Print) | 0302-9743 |

### Conference

Conference | 21st Annual European Symposium on Algorithms (ESA 2013) |
---|---|

Abbreviated title | ESA 2013 |

Country | France |

City | Sophia Antipolis |

Period | 2/09/13 → 4/09/13 |

Internet address |

## Cite this

Buchin, K., Buchin, M., Leusden, van, R., Meulemans, W., & Mulzer, W. (2013). Computing the Fréchet distance with a retractable leash. In H. L. Bodlaender, & G. F. Italiano (Eds.),

*21st Annual European Symposium on Algorithms (ESA)*(pp. 241-252). (Lecture Notes in Computer Science; Vol. 8125). Springer. https://doi.org/10.1007/978-3-642-40450-4_21