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Counting Polygon Triangulations is Hard

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Abstract

We prove that it is \(\#{\mathsf {P}}\)-complete to count the triangulations of a (non-simple) polygon.

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Notes

  1. See Sect. 2.2 for the definitions of \(\#{\mathsf {P}}\) and \(\#{\mathsf {P}}\)-completeness.

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Acknowledgements

A preliminary version of this paper appeared in the Proceedings of the 2019 International Symposium on Computational Geometry. This work was supported in part by the US National Science Foundation under Grants CCF-1618301 and CCF-1616248.

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  1. Computer Science Department, University of California, Irvine, USA

    David Eppstein

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Eppstein, D. Counting Polygon Triangulations is Hard. Discrete Comput Geom 64, 1210–1234 (2020). https://doi.org/10.1007/s00454-020-00251-7

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