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Minimum Convex Partition of a Polygon with Holes by Cuts in Given Directions

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Abstract.

Let \({\cal F}\) be a given family of directions in the plane. The problem of partitioning a planar polygon P with holes into a minimum number of convex polygons by cuts in the directions of \({\cal F}\) is proved to be NP-hard if \(|{\cal F}| \ge 3\) and it is shown to admit a polynomial-time algorithm if \(|{\cal F}| \le 2\) .

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Authors and Affiliations

  1. Department of Computer Science, Lund University, S-22100 Lund, Sweden , , , , , , SE

    A. Lingas

  2. Mathematical Institute, Academy of Sciences, MD-20028 Chişinău, Moldova, , , , , , MD

    V. Soltan

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  1. A. Lingas
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  2. V. Soltan
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Received February 1997, and in revised form November 1997, and in final form February 1998.

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Lingas, A., Soltan, V. Minimum Convex Partition of a Polygon with Holes by Cuts in Given Directions . Theory Comput. Systems 31, 507–538 (1998). https://doi.org/10.1007/s002240000101

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  • DOI: https://doi.org/10.1007/s002240000101

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