Abstract
We describe a randomized algorithm for computing the trapezoidal decomposition of a simple polygon. Its expected running time is linear in the size of the polygon. By a well-known and simple linear time reduction, this implies a linear time algorithm for triangulating a simple polygon. Our algorithm is considerably simpler than Chazelle’s [3] celebrated optimal deterministic algorithm. The new algorithm can be viewed as a combination of Chazelle’s algorithm and of simple nonoptimal randomized algorithms due to Clarkson et al. [6], [7], [9] and to Seidel [20]. As in Chazelle’s algorithm, it is indispensable to include a bottom-up preprocessing phase, in addition to the actual top-down construction. An essential new idea is the use of random sampling on subchains of the initial polygonal chain, rather than on individual edges as is normally done.
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Received April 18, 2000, and in revised form December 7, 2000. Online publication June 20, 2001.
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Amato, N., Goodrich, M. & Ramos, E. A Randomized Algorithm for Triangulating a Simple Polygon in Linear Time. Discrete Comput Geom 26, 245–265 (2001). https://doi.org/10.1007/s00454-001-0027-x
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DOI: https://doi.org/10.1007/s00454-001-0027-x