Finding the Medial Axis of a Simple Polygon in Linear Time

We give a linear-time algorithm for computing the medial axis of a simple polygon P, This answers a long-standing open question—previously, the best deterministic algorithm ran in O(n log n) time. We decompose P into pseudo-normal histograms, then influence histograms and xy monotone histograms. We can compute the medial axes for xy monotone histograms and merge to obtain the medial axis for P.

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