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 innuence histograms and xy monotone histograms. We can compute the medial axes for xy monotone his-tograms and merge to obtain the medial axis for P.
