### Abstract

We give deterministic and randomized algorithms to find shortest paths homotopic to a given collection Π of disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k _{out}+k _{in}logn+n√n), and the randomized algorithm runs in expected time O(k _{out}+k ^{in}logn+n(logn) ^{1+ε}). Here k ^{in} is the number of edges in all the paths of Π, and k ^{out} is the number of edges in the output paths.

Original language | English (US) |
---|---|

Pages (from-to) | 162-172 |

Number of pages | 11 |

Journal | Computational Geometry: Theory and Applications |

Volume | 35 |

Issue number | 3 |

DOIs | |

State | Published - Oct 2006 |

### Fingerprint

### Keywords

- Homotopic shortest paths
- Shortest path in a polygon

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Computational Mathematics
- Control and Optimization
- Geometry and Topology

### Cite this

*Computational Geometry: Theory and Applications*,

*35*(3), 162-172. https://doi.org/10.1016/j.comgeo.2006.03.003

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

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 35, no. 3, pp. 162-172. https://doi.org/10.1016/j.comgeo.2006.03.003

}

TY - JOUR

T1 - Computing homotopic shortest paths efficiently

AU - Efrat, Alon

AU - Kobourov, Stephen G

AU - Lubiw, Anna

PY - 2006/10

Y1 - 2006/10

N2 - We give deterministic and randomized algorithms to find shortest paths homotopic to a given collection Π of disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k out+k inlogn+n√n), and the randomized algorithm runs in expected time O(k out+k inlogn+n(logn) 1+ε). Here k in is the number of edges in all the paths of Π, and k out is the number of edges in the output paths.

AB - We give deterministic and randomized algorithms to find shortest paths homotopic to a given collection Π of disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k out+k inlogn+n√n), and the randomized algorithm runs in expected time O(k out+k inlogn+n(logn) 1+ε). Here k in is the number of edges in all the paths of Π, and k out is the number of edges in the output paths.

KW - Homotopic shortest paths

KW - Shortest path in a polygon

UR - http://www.scopus.com/inward/record.url?scp=84867977487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867977487&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2006.03.003

DO - 10.1016/j.comgeo.2006.03.003

M3 - Article

AN - SCOPUS:84867977487

VL - 35

SP - 162

EP - 172

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 3

ER -