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Are there by now simpler algorithms/proofs for triangulating a planar polygon in linear time? What is a good resource on the state of the art of this famous problem?

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So far, the only improvement to Chazelle's juggernaut is the 2001 randomized linear-time algorithm by Amato, Goodrich, and Ramos. Chazelle's algorithm is still the only deterministic O(n)-time triangulation algorithm known.

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