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AN O(n log log n)-TIME ALGORITHM FOR TRIANGULATING A SIMPLE POLYGON

By Robert E. Tarjan and Christopher J. Van Wyk

Abstract

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 logn)-time algorithm for this problem, improving on the previously 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

Year: 1988
OAI identifier: oai:CiteSeerX.psu:10.1.1.186.5949
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