Polygon triangulation in O(n log log n) time with simple data-structures

We give a new &Ogr;(n log log n)-time deterministic linear-time algorithm for triangulating simple n-vertex polygons, which avoids the use of complicated data-structures. In addition, for polygons whose vertices have integer coordinates of polynomially bounded size, the algorithm can be modified to run in &Ogr;(n log* n) time. The major new techniques employed are the efficient location of horizontal visibility edges which partition the interior of the polygon into regions of approximately equal size, and a linear-time algorithm for obtaining the horizontal visibility partition of a subchain of a polygonal chain, from the horizontal visibility partition of the entire chain. This latter technique has other interesting applications, including a linear-time algorithm to convert a Steiner triangulation of a polygon into a true triangulation. This research was partially supported by DIMACS and the following grants: NSERC 583584, NSERC 580485, NSF-STC88-09648, ONR-N00014-87-0467.