### 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(
^{n2}logn) 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)logn+(n/ ε3
^{/2})
^{log2}(1/ε)). A much simpler constant-factor approximation algorithm is also described.

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

Pages (from-to) | 298-309 |

Number of pages | 12 |

Journal | Computational Geometry: Theory and Applications |

Volume | 46 |

Issue number | 3 |

DOIs | |

State | Published - Apr 2013 |

### Fingerprint

### Keywords

- Approximation algorithm
- Computational metrology
- Curve reconstruction
- Fitting
- Geometric optimization

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Computational Mathematics
- Control and Optimization
- Geometry and Topology

### Cite this

*Computational Geometry: Theory and Applications*,

*46*(3), 298-309. https://doi.org/10.1016/j.comgeo.2012.09.006

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

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 46, no. 3, pp. 298-309. https://doi.org/10.1016/j.comgeo.2012.09.006

}

TY - JOUR

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

AU - Aronov, Boris

AU - Dulieu, Muriel

PY - 2013/4

Y1 - 2013/4

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( n2logn) 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)logn+(n/ ε3 /2) log2(1/ε)). A much simpler constant-factor approximation algorithm is also described.

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( n2logn) 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)logn+(n/ ε3 /2) log2(1/ε)). A much simpler constant-factor approximation algorithm is also described.

KW - Approximation algorithm

KW - Computational metrology

KW - Curve reconstruction

KW - Fitting

KW - Geometric optimization

UR - http://www.scopus.com/inward/record.url?scp=84869094244&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869094244&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2012.09.006

DO - 10.1016/j.comgeo.2012.09.006

M3 - Article

VL - 46

SP - 298

EP - 309

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 3

ER -