### Abstract

We present a collection of algorithms, all running in time O(n^{2} log n α (n)^{o(α(n)3)}) for some fixed integer s(where α(n) is the inverse Ackermann's function), for constructing a skeleton representation of a suitably generalized "Voronoi diagram" for a ladder moving in a two-dimensional space bounded by polygonal barriers consisting of n line segments. This diagram, which is a two-dimensional subcomplex of the dimensional configuration space of the ladder, is introduced and analyzed in a companion paper by the present authors. The construction of the diagram described in this paper yields a motion-planning algorithm for the ladder which runs within the same time bound given above.

Original language | English (US) |
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Pages (from-to) | 27-59 |

Number of pages | 33 |

Journal | Algorithmica (New York) |

Volume | 2 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1987 |

### Fingerprint

### Keywords

- Configuration space
- Motion planning
- Moving ladder
- Robotics
- Voronoi diagram

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Safety, Risk, Reliability and Quality
- Applied Mathematics

### Cite this

*Algorithmica (New York)*,

*2*(1), 27-59. https://doi.org/10.1007/BF01840348

**Generalized Voronoi diagrams for a ladder : II. Efficient construction of the diagram.** / Ó'Dúnlaing, Colm; Sharir, Micha; Yap, Chee.

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 2, no. 1, pp. 27-59. https://doi.org/10.1007/BF01840348

}

TY - JOUR

T1 - Generalized Voronoi diagrams for a ladder

T2 - II. Efficient construction of the diagram

AU - Ó'Dúnlaing, Colm

AU - Sharir, Micha

AU - Yap, Chee

PY - 1987/3

Y1 - 1987/3

N2 - We present a collection of algorithms, all running in time O(n2 log n α (n)o(α(n)3)) for some fixed integer s(where α(n) is the inverse Ackermann's function), for constructing a skeleton representation of a suitably generalized "Voronoi diagram" for a ladder moving in a two-dimensional space bounded by polygonal barriers consisting of n line segments. This diagram, which is a two-dimensional subcomplex of the dimensional configuration space of the ladder, is introduced and analyzed in a companion paper by the present authors. The construction of the diagram described in this paper yields a motion-planning algorithm for the ladder which runs within the same time bound given above.

AB - We present a collection of algorithms, all running in time O(n2 log n α (n)o(α(n)3)) for some fixed integer s(where α(n) is the inverse Ackermann's function), for constructing a skeleton representation of a suitably generalized "Voronoi diagram" for a ladder moving in a two-dimensional space bounded by polygonal barriers consisting of n line segments. This diagram, which is a two-dimensional subcomplex of the dimensional configuration space of the ladder, is introduced and analyzed in a companion paper by the present authors. The construction of the diagram described in this paper yields a motion-planning algorithm for the ladder which runs within the same time bound given above.

KW - Configuration space

KW - Motion planning

KW - Moving ladder

KW - Robotics

KW - Voronoi diagram

UR - http://www.scopus.com/inward/record.url?scp=0023231839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023231839&partnerID=8YFLogxK

U2 - 10.1007/BF01840348

DO - 10.1007/BF01840348

M3 - Article

VL - 2

SP - 27

EP - 59

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 1

ER -