### Abstract

We give algorithms to find shortest paths homotopic to given disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k log n+n√n), and the randomized version in time O(k log n + n(logn)<sup>1+ε</sup>), where k is the input plus output sizes of the paths.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 411-423 |

Number of pages | 13 |

Volume | 2461 |

ISBN (Print) | 3540441808, 9783540441809 |

State | Published - 2002 |

Event | 10th Annual European Symposium on Algorithms, ESA 2002 - Rome, Italy Duration: Sep 17 2002 → Sep 21 2002 |

### 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 | 2461 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 10th Annual European Symposium on Algorithms, ESA 2002 |
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Country | Italy |

City | Rome |

Period | 9/17/02 → 9/21/02 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 2461, pp. 411-423). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2461). Springer Verlag.

**Computing homotopic shortest paths efficiently.** / Efrat, Alon; Kobourov, Stephen G; Lubiw, Anna.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 2461, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2461, Springer Verlag, pp. 411-423, 10th Annual European Symposium on Algorithms, ESA 2002, Rome, Italy, 9/17/02.

}

TY - GEN

T1 - Computing homotopic shortest paths efficiently

AU - Efrat, Alon

AU - Kobourov, Stephen G

AU - Lubiw, Anna

PY - 2002

Y1 - 2002

N2 - We give algorithms to find shortest paths homotopic to given disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k log n+n√n), and the randomized version in time O(k log n + n(logn)1+ε), where k is the input plus output sizes of the paths.

AB - We give algorithms to find shortest paths homotopic to given disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k log n+n√n), and the randomized version in time O(k log n + n(logn)1+ε), where k is the input plus output sizes of the paths.

UR - http://www.scopus.com/inward/record.url?scp=84938062776&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938062776&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84938062776

SN - 3540441808

SN - 9783540441809

VL - 2461

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

SP - 411

EP - 423

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

PB - Springer Verlag

ER -