### 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) |
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Pages (from-to) | 162-172 |

Number of pages | 11 |

Journal | Computational Geometry: Theory and Applications |

Volume | 35 |

Issue number | 3 |

DOIs | |

State | Published - Oct 1 2006 |

### Keywords

- Homotopic shortest paths
- Shortest path in a polygon

### ASJC Scopus subject areas

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

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## Cite this

Efrat, A., Kobourov, S. G., & Lubiw, A. (2006). Computing homotopic shortest paths efficiently.

*Computational Geometry: Theory and Applications*,*35*(3), 162-172. https://doi.org/10.1016/j.comgeo.2006.03.003