### Abstract

The problem of cutting a convex polygon P out of a piece of planar material Q with minimum total cutting length is a well studied problem in computational geometry. Researchers studied several variations of the problem, such as P and Q are convex or non-convex polygons and the cuts are line cuts or ray cuts. In this paper we consider yet another variation of the problem where Q is a circle and P is a convex polygon such that P is bounded by a half circle of Q and all the cuts are line cuts. We give two algorithms for solving this problem. Our first algorithm is an O(log n)-approximation algorithm with O(n) running time, where n is the number of edges of P. The second algorithm is a constant factor approximation algorithm with approximation ratio 6.48 and running time O(n^{3}).

Original language | English |
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Pages (from-to) | 4-11 |

Number of pages | 8 |

Journal | Journal of Computers |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2010 |

### Keywords

- Algorithms
- Approximation algorithms
- Computational geometry
- Line cut
- Polygon cutting
- Ray cut
- Rotating calipers

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## Cite this

*Journal of Computers*,

*5*(1), 4-11. https://doi.org/10.4304/jcp.5.1.4-11