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Recognizing Weakly Simple Polygons

Authors Hugo A. Akitaya, Greg Aloupis, Jeff Erickson, Csaba Tóth

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Hugo A. Akitaya
Greg Aloupis
Jeff Erickson
Csaba Tóth

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Hugo A. Akitaya, Greg Aloupis, Jeff Erickson, and Csaba Tóth. Recognizing Weakly Simple Polygons. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 8:1-8:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


We present an O(n log n)-time algorithm that determines whether a given planar n-gon is weakly simple. This improves upon an O(n^2 log n)-time algorithm by [Chang, Erickson, and Xu, SODA, 2015]. Weakly simple polygons are required as input for several geometric algorithms. As such, how to recognize simple or weakly simple polygons is a fundamental question.
  • weakly simple polygon
  • crossing


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  1. Hugo A. Akitaya, Greg Aloupis, Jeff Erickson, and Csaba D. Tóth. Recognizing weakly simple polygons. Preprint, 2016. URL:
  2. Esther M. Arkin, Michael A. Bender, Erik D. Demaine, Martin L. Demaine, Joseph S.B. Mitchell, Saurabh Sethia, and Steven S. Skiena. When can you fold a map? Computational Geometry, 29(1):23-46, 2004. Google Scholar
  3. Marshall Bern and Barry Hayes. The complexity of flat origami. In Proc. 7th ACM-SIAM Sympos. on Discrete Algorithms, pages 175-183, 1996. Google Scholar
  4. Hsien-Chih Chang, Jeff Erickson, and Chao Xu. Detecting weakly simple polygons. In Proc. 26th ACM-SIAM Sympos. on Discrete Algorithms, pages 1655-1670, 2015. Google Scholar
  5. Bernard Chazelle. Triangulating a simple polygon in linear time. Discrete Comput. Geom., 6(3):485-524, 1991. Google Scholar
  6. Pier Francesco Cortese, Giuseppe Di Battista, Maurizio Patrignani, and Maurizio Pizzonia. On embedding a cycle in a plane graph. Discrete Math., 309(7):1856-1869, 2009. Google Scholar
  7. Ares Ribó Mor. Realization and counting problems for planar structures. PhD thesis, Freie Universität Berlin, Department of Mathematics and Computer Science, 2006. Google Scholar
  8. Michael Ian Shamos and Dan Hoey. Geometric intersection problems. In Proc. 17th IEEE Sympos. Foundations of Computer Science, pages 208-215, 1976. Google Scholar
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