## Abstract

Given a convex polytope P with n faces in ℝ^{3}, points s, t ∈ ∂P, and a parameter 0 < ∈ ≤ 1, we present an algorithm that constructs a path on ∂P from s to t whose length is at most (1 + ∈)d_{P}(s, t), where d_{P}(s, t) is the length of the shortest path between s and t on ∂P. The algorithm runs in O(n log 1/∈ + 1/∈^{3}) time, and is relatively simple. The running time is O(n + 1/∈^{3}) if we only want the approximate shortest path distance and not the path itself. We also present an extension of the algorithm that computes approximate shortest path distances from a given source point on ∂P to all vertices of P.

Original language | English (US) |
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Pages (from-to) | 567-584 |

Number of pages | 18 |

Journal | Journal of the ACM |

Volume | 44 |

Issue number | 4 |

DOIs | |

State | Published - Jul 1997 |

Externally published | Yes |

## Keywords

- Algorithms
- Approximation algorithms
- Convex polytopes
- Euclidean shortest paths
- Theory

## ASJC Scopus subject areas

- Software
- Control and Systems Engineering
- Information Systems
- Hardware and Architecture
- Artificial Intelligence