### Abstract

Given two finite sets of points in a plane, the polygon separation problem is to construct a separating convex k-gon with smallest k. In this paper, we present a parallel algorithm for the polygon separation problem. The algorithm runs in O(log n) time on a CREW PRAM with n processors, where n is the number of points in the two given sets. The algorithm is cost-optimal, since Ω(n log n) is a lower-bound for the time needed by any sequential algorithm. We apply this algorithm to the problem of finding a convex polygon, with the minimal number of edges, for which a given convex region is its digital image. The algorithm in this paper constructs one such polygon with possibly two more edges than the minimal one.

Original language | English (US) |
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Pages (from-to) | 109-121 |

Number of pages | 13 |

Journal | International Journal of Parallel Programming |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 1992 |

### Keywords

- Algorithms
- PRAMs
- computational geometry
- digital polygons
- parallel algorithms

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Information Systems

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## Cite this

*International Journal of Parallel Programming*,

*21*(2), 109-121. https://doi.org/10.1007/BF01408289