Geodesic diameter of a polygonal domain in O(n^4 log n) time

Abstract

We show that the geodesic diameter of a polygonal domain with n vertices can be computed in O(n^4 log n) time by considering O(n^3) candidate diameter endpoints; the endpoints are a subset of vertices of the overlay of shortest path maps from vertices of the domain.

arXiv commentNOTE: It has turned out that, unfortunately, Lemma 2 does not hold, which renders the main result incorrect