Finding the medial axis of a simple polygon in linear time

Abstract

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 pseudonormal histograms, then influence histograms, then xy monotone histograms. We can compute the medial axes for xy monotone histograms and merge to obtain the medial axis for P.