O(n log log n)-time algorithm for triangulating a simple polygon

Robert E. Tarjan, Christopher J. Van Wyk

Research output: Contribution to journalArticlepeer-review

121 Scopus citations


Given a simple n-vertex polygon, the triangulation problem is to partition the interior of the polygon into n-2 triangles by adding n-3 nonintersecting diagonals. We propose an O(n log log n)-time algorithm for this problem, improving on the previous best bound of O(n log n) and showing that triangulation is not as hard as sorting Improved algorithms for several other computational geometry problems, including testing whether a polygon is simple, follow from our result.

Original languageEnglish (US)
Pages (from-to)143-178
Number of pages36
JournalSIAM Journal on Computing
Issue number1
StatePublished - 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • General Mathematics


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