### Abstract

We give a combinatorial definition of the notion of a simple orthogonal polygon being k-concave, where k is a nonnegative integer. (A polygon is orthogonal if its edges are only horizontal or vertical.) Under this definition an orthogonal polygon which is 0-concave is convex, that is, it is a rectangle, and one that is 1-concave is orthoconvex in the usual sense, and vice versa. Then we consider the problem of computing an orthoconvex orthogonal polygon of maximal area contained in a simple orthogonal polygon. This is the orthogonal version of the potato peeling problem. An O(n^{2}) algorithm is presented, which is a substantial improvement over the O(n^{7}) time algorithm for the general problem.

Original language | English (US) |
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Pages (from-to) | 349-365 |

Number of pages | 17 |

Journal | Discrete & Computational Geometry |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1988 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

*Discrete & Computational Geometry*,

*3*(1), 349-365. https://doi.org/10.1007/BF02187918