### Abstract

Let B be any finite set of pairwise-disjoint, axes-parallel boxes in Euclidean d-space. Our main theorem is that for any two points s, t not in the interior of B, there exists a coordinate direction φ such that every rectilinear B-avoiding shortest path is monotone along φ. The key concept in the proof is an appropriate notion of pyramids.

Original language | English (US) |
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Pages | 339-348 |

Number of pages | 10 |

State | Published - Jan 1 1996 |

Event | Proceedings of the 1996 12th Annual Symposium on Computational Geometry - Philadelphia, PA, USA Duration: May 24 1996 → May 26 1996 |

### Other

Other | Proceedings of the 1996 12th Annual Symposium on Computational Geometry |
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City | Philadelphia, PA, USA |

Period | 5/24/96 → 5/26/96 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

Choi, J., & Yap, C. K. (1996).

*Monotonicity of rectilinear geodesics in d-space*. 339-348. Paper presented at Proceedings of the 1996 12th Annual Symposium on Computational Geometry, Philadelphia, PA, USA, .