### Abstract

We study the space of free translations of a box amidst polyhedral obstacles with n features. We show that the combinatorial complexity of this space is O(n
^{2}α(n)) where α(n) is the inverse Ackermann function. Our bound is within an α(n) factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, O(n
^{3}).

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

Title of host publication | Proceedings of the 9th Annual Symposium on Computational Geometry |

Editors | Anon |

Publisher | Publ by ACM |

Pages | 29-37 |

Number of pages | 9 |

ISBN (Print) | 0897915828 |

State | Published - 1993 |

Event | Proceedings of the 9th Annual Symposium on Computational Geometry - San Diego, CA, USA Duration: May 19 1993 → May 21 1993 |

### Other

Other | Proceedings of the 9th Annual Symposium on Computational Geometry |
---|---|

City | San Diego, CA, USA |

Period | 5/19/93 → 5/21/93 |

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the 9th Annual Symposium on Computational Geometry*(pp. 29-37). Publ by ACM.

**Combinatorial complexity of translating a box in polyhedral 3-space.** / Halperin, Dan; Yap, Chee.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 9th Annual Symposium on Computational Geometry.*Publ by ACM, pp. 29-37, Proceedings of the 9th Annual Symposium on Computational Geometry, San Diego, CA, USA, 5/19/93.

}

TY - GEN

T1 - Combinatorial complexity of translating a box in polyhedral 3-space

AU - Halperin, Dan

AU - Yap, Chee

PY - 1993

Y1 - 1993

N2 - We study the space of free translations of a box amidst polyhedral obstacles with n features. We show that the combinatorial complexity of this space is O(n 2α(n)) where α(n) is the inverse Ackermann function. Our bound is within an α(n) factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, O(n 3).

AB - We study the space of free translations of a box amidst polyhedral obstacles with n features. We show that the combinatorial complexity of this space is O(n 2α(n)) where α(n) is the inverse Ackermann function. Our bound is within an α(n) factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, O(n 3).

UR - http://www.scopus.com/inward/record.url?scp=0027803463&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027803463&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0897915828

SP - 29

EP - 37

BT - Proceedings of the 9th Annual Symposium on Computational Geometry

A2 - Anon, null

PB - Publ by ACM

ER -