### Abstract

The problem of cutting a convex polygon P out of a planar piece of material Q (P is already drawn on Q) with minimum total cutting cost is a well studied problem in computational geometry that has been studied with several variations such as P and Q are convex or non-convex polygons, Q is a circle, and the cuts are line cuts or ray cuts. In this paper, we address this problem without the restriction that P is fixed inside Q and consider the variation where Q is a circle and the cuts are line cuts. We show that if P can be placed inside Q such that P does not contain the center of Q, then placing P in a most cornered position inside Q gives a cutting cost of 6.48 times the optimal. We also give an O(n ^{2})-time algorithm for finding such a position of P, a problem that may be of independent interest. When any placement of P must contain the center of Q, we show that P can be cut of Q with cost 6.054 times the optimal.

Original language | English |
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Title of host publication | WALCOM |

Subtitle of host publication | Algorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings |

Pages | 252-262 |

Number of pages | 11 |

DOIs | |

Publication status | Published - 25 Mar 2010 |

Event | 4th International Workshop on Algorithms and Computation, WALCOM 2010 - Dhaka, Bangladesh Duration: 10 Feb 2010 → 12 Feb 2010 |

### 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 | 5942 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 4th International Workshop on Algorithms and Computation, WALCOM 2010 |
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Country | Bangladesh |

City | Dhaka |

Period | 10/2/10 → 12/2/10 |

### Keywords

- Cornerable and non-cornerable polygon
- Cutting cost
- Line cut
- Most cornered position
- Polygon cutting

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*WALCOM: Algorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings*(pp. 252-262). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5942 LNCS). https://doi.org/10.1007/978-3-642-11440-3_23