### Abstract

Most motion planning problems, except for the simplest examples, have at least a quadratic time complexity in the worst case. Our study is motivated by the attempt to reduce the complexity of the polygon containment problem, and also the motion planning problem. In each case, we describe algorithms which will run faster when certain implicit slackness parameters of the input are bounded away from 1. These algorithms illustrate a new algorithmic paradigm in computational geometry for coping with complexity.

Original language | English (US) |
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Title of host publication | Proc Sixth Annu Symp Comput Geom |

Publisher | Publ by ACM |

Pages | 216-224 |

Number of pages | 9 |

ISBN (Print) | 0897913620 |

State | Published - 1990 |

Event | Proceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA Duration: Jun 6 1990 → Jun 8 1990 |

### Other

Other | Proceedings of the Sixth Annual Symposium on Computational Geometry |
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City | Berkeley, CA, USA |

Period | 6/6/90 → 6/8/90 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proc Sixth Annu Symp Comput Geom*(pp. 216-224). Publ by ACM.

**On simultaneous inner and outer approximation of shapes.** / Fleischer, Rudolf; Mehlhorn, Kurt; Rote, Gunter; Welzl, Emo; Yap, Chee.

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

*Proc Sixth Annu Symp Comput Geom.*Publ by ACM, pp. 216-224, Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, CA, USA, 6/6/90.

}

TY - GEN

T1 - On simultaneous inner and outer approximation of shapes

AU - Fleischer, Rudolf

AU - Mehlhorn, Kurt

AU - Rote, Gunter

AU - Welzl, Emo

AU - Yap, Chee

PY - 1990

Y1 - 1990

N2 - Most motion planning problems, except for the simplest examples, have at least a quadratic time complexity in the worst case. Our study is motivated by the attempt to reduce the complexity of the polygon containment problem, and also the motion planning problem. In each case, we describe algorithms which will run faster when certain implicit slackness parameters of the input are bounded away from 1. These algorithms illustrate a new algorithmic paradigm in computational geometry for coping with complexity.

AB - Most motion planning problems, except for the simplest examples, have at least a quadratic time complexity in the worst case. Our study is motivated by the attempt to reduce the complexity of the polygon containment problem, and also the motion planning problem. In each case, we describe algorithms which will run faster when certain implicit slackness parameters of the input are bounded away from 1. These algorithms illustrate a new algorithmic paradigm in computational geometry for coping with complexity.

UR - http://www.scopus.com/inward/record.url?scp=0024984188&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024984188&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0024984188

SN - 0897913620

SP - 216

EP - 224

BT - Proc Sixth Annu Symp Comput Geom

PB - Publ by ACM

ER -