### Abstract

We solve the problem of computing the shortest closed path inside a given polygon which visits every edge at least once (Aquarium Keeper's Tour). For convex polygons, we present a linear-time algorithm which uses the reflection principle and shortest-path maps. We then generalize that method by using relative convex hulls to provide a linear algorithm for polygons which are not convex.

Original language | English (US) |
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Title of host publication | Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991 |

Publisher | Association for Computing Machinery |

Pages | 459-464 |

Number of pages | 6 |

Volume | Part F129903 |

ISBN (Print) | 0897913760 |

State | Published - Mar 1 1991 |

Event | 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991 - San Francisco, United States Duration: Jan 28 1991 → Jan 30 1991 |

### Other

Other | 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991 |
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Country | United States |

City | San Francisco |

Period | 1/28/91 → 1/30/91 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991*(Vol. Part F129903, pp. 459-464). Association for Computing Machinery.

**The Aquarium Keeper's problem.** / Czyzowicz, Jurek; Egyed, Peter; Everett, Hazel; Rappaport, David; Shermer, Thomas; Souvaine, Diane; Toussaint, Godfried; Urrutia, Jorge.

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

*Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991.*vol. Part F129903, Association for Computing Machinery, pp. 459-464, 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991, San Francisco, United States, 1/28/91.

}

TY - GEN

T1 - The Aquarium Keeper's problem

AU - Czyzowicz, Jurek

AU - Egyed, Peter

AU - Everett, Hazel

AU - Rappaport, David

AU - Shermer, Thomas

AU - Souvaine, Diane

AU - Toussaint, Godfried

AU - Urrutia, Jorge

PY - 1991/3/1

Y1 - 1991/3/1

N2 - We solve the problem of computing the shortest closed path inside a given polygon which visits every edge at least once (Aquarium Keeper's Tour). For convex polygons, we present a linear-time algorithm which uses the reflection principle and shortest-path maps. We then generalize that method by using relative convex hulls to provide a linear algorithm for polygons which are not convex.

AB - We solve the problem of computing the shortest closed path inside a given polygon which visits every edge at least once (Aquarium Keeper's Tour). For convex polygons, we present a linear-time algorithm which uses the reflection principle and shortest-path maps. We then generalize that method by using relative convex hulls to provide a linear algorithm for polygons which are not convex.

UR - http://www.scopus.com/inward/record.url?scp=85032002331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032002331&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85032002331

SN - 0897913760

VL - Part F129903

SP - 459

EP - 464

BT - Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1991

PB - Association for Computing Machinery

ER -