### Abstract

A balanced V-shape is a polygonal region in the plane contained in the union of two crossing equal-width strips. It is delimited by two pairs of parallel rays that emanate from two points x, y, are contained in the strip boundaries, and are mirror-symmetric with respect to the line xy. The width of a balanced V-shape is the width of the strips. We first present an O(n
^{2} log n) time algorithm to compute, given a set of n points P, a minimum-width balanced V-shape covering P. We then describe a PTAS for computing a (1 + ε)-approximation of this V-shape in time O((n/ε)log n + (n/ε
^{3/2})log
^{2}(1/ε)).

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings |

Pages | 61-72 |

Number of pages | 12 |

Volume | 6844 LNCS |

DOIs | |

State | Published - 2011 |

Event | 12th International Symposium on Algorithms and Data Structures, WADS 2011 - New York, NY, United States Duration: Aug 15 2011 → Aug 17 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6844 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 12th International Symposium on Algorithms and Data Structures, WADS 2011 |
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Country | United States |

City | New York, NY |

Period | 8/15/11 → 8/17/11 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings*(Vol. 6844 LNCS, pp. 61-72). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6844 LNCS). https://doi.org/10.1007/978-3-642-22300-6_6

**How to cover a point set with a V-shape of minimum width.** / Aronov, Boris; Dulieu, Muriel.

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

*Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings.*vol. 6844 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6844 LNCS, pp. 61-72, 12th International Symposium on Algorithms and Data Structures, WADS 2011, New York, NY, United States, 8/15/11. https://doi.org/10.1007/978-3-642-22300-6_6

}

TY - GEN

T1 - How to cover a point set with a V-shape of minimum width

AU - Aronov, Boris

AU - Dulieu, Muriel

PY - 2011

Y1 - 2011

N2 - A balanced V-shape is a polygonal region in the plane contained in the union of two crossing equal-width strips. It is delimited by two pairs of parallel rays that emanate from two points x, y, are contained in the strip boundaries, and are mirror-symmetric with respect to the line xy. The width of a balanced V-shape is the width of the strips. We first present an O(n 2 log n) time algorithm to compute, given a set of n points P, a minimum-width balanced V-shape covering P. We then describe a PTAS for computing a (1 + ε)-approximation of this V-shape in time O((n/ε)log n + (n/ε 3/2)log 2(1/ε)).

AB - A balanced V-shape is a polygonal region in the plane contained in the union of two crossing equal-width strips. It is delimited by two pairs of parallel rays that emanate from two points x, y, are contained in the strip boundaries, and are mirror-symmetric with respect to the line xy. The width of a balanced V-shape is the width of the strips. We first present an O(n 2 log n) time algorithm to compute, given a set of n points P, a minimum-width balanced V-shape covering P. We then describe a PTAS for computing a (1 + ε)-approximation of this V-shape in time O((n/ε)log n + (n/ε 3/2)log 2(1/ε)).

UR - http://www.scopus.com/inward/record.url?scp=80052125797&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052125797&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-22300-6_6

DO - 10.1007/978-3-642-22300-6_6

M3 - Conference contribution

SN - 9783642222993

VL - 6844 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 61

EP - 72

BT - Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings

ER -