## Abstract

We revisit the problem of computing shortest obstacle-avoiding paths among obstacles in three dimensions. We prove new hardness results, showing, e.g., that computing Euclidean shortest paths among sets of "stacked" axis-aligned rectangles is NP-complete, and that computing L _{1}-shortest paths among disjoint balls is NP-complete. On the positive side, we present an efficient algorithm for computing an L _{1}shortest path between two given points that lies on or above a given polyhedral terrain. We also give polynomial-time algorithms for some versions of stacked polygonal obstacles that are "terrain-like" and analyze the complexity of shortest path maps in the presence of parallel halfplane "walls".

Original language | English |
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Pages | 124-133 |

Number of pages | 10 |

DOIs | |

State | Published - 2004 |

Event | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States Duration: 9 Jun 2004 → 11 Jun 2004 |

### Conference

Conference | Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) |
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Country/Territory | United States |

City | Brooklyn, NY |

Period | 9/06/04 → 11/06/04 |

## Keywords

- Motion planning
- NP-hardness
- Shortest path
- Terrain