### Abstract

We revisit the problem of computing the Fréchet distance between polygonal curves, focusing on the discrete Fréchet distance, where only distance between vertices is considered. We develop efficient approximation algorithms for two natural classes of curves: κ-bounded curves and backbone curves, the latter of which are widely used to model molecular structures. We also propose a pseudo-output-sensitive algorithm for computing the discrete Fréchet distance exactly. The complexity of the algorithm is a function of the complexity of the free-space boundary, which is quadratic in the worst case, but tends to be lower in practice.

Original language | English (US) |
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Title of host publication | Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings |

Pages | 52-63 |

Number of pages | 12 |

Volume | 4168 LNCS |

State | Published - 2006 |

Event | 14th Annual European Symposium on Algorithms, ESA 2006 - Zurich, Switzerland Duration: Sep 11 2006 → Sep 13 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4168 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 14th Annual European Symposium on Algorithms, ESA 2006 |
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Country | Switzerland |

City | Zurich |

Period | 9/11/06 → 9/13/06 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings*(Vol. 4168 LNCS, pp. 52-63). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4168 LNCS).

**Fréchet distance for curves, revisited.** / Aronov, Boris; Har-Peled, Sariel; Knauer, Christian; Wang, Yusu; Wenk, Carola.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings.*vol. 4168 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4168 LNCS, pp. 52-63, 14th Annual European Symposium on Algorithms, ESA 2006, Zurich, Switzerland, 9/11/06.

}

TY - GEN

T1 - Fréchet distance for curves, revisited

AU - Aronov, Boris

AU - Har-Peled, Sariel

AU - Knauer, Christian

AU - Wang, Yusu

AU - Wenk, Carola

PY - 2006

Y1 - 2006

N2 - We revisit the problem of computing the Fréchet distance between polygonal curves, focusing on the discrete Fréchet distance, where only distance between vertices is considered. We develop efficient approximation algorithms for two natural classes of curves: κ-bounded curves and backbone curves, the latter of which are widely used to model molecular structures. We also propose a pseudo-output-sensitive algorithm for computing the discrete Fréchet distance exactly. The complexity of the algorithm is a function of the complexity of the free-space boundary, which is quadratic in the worst case, but tends to be lower in practice.

AB - We revisit the problem of computing the Fréchet distance between polygonal curves, focusing on the discrete Fréchet distance, where only distance between vertices is considered. We develop efficient approximation algorithms for two natural classes of curves: κ-bounded curves and backbone curves, the latter of which are widely used to model molecular structures. We also propose a pseudo-output-sensitive algorithm for computing the discrete Fréchet distance exactly. The complexity of the algorithm is a function of the complexity of the free-space boundary, which is quadratic in the worst case, but tends to be lower in practice.

UR - http://www.scopus.com/inward/record.url?scp=33750699629&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750699629&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33750699629

SN - 3540388753

SN - 9783540388753

VL - 4168 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 52

EP - 63

BT - Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings

ER -