@article{4115,
abstract = {A polygon in the plane is convex if it contains all line segments connecting any two of its points. Let P and Q denote two convex polygons. The computational complexity of finding the minimum and maximum distance possible between two points p in P and q in Q is studied. An algorithm is described that determines the minimum distance (together with points p and q that realize it) in O(logm + logn) time, where m and n denote the number of vertices of P and Q, respectively. This is optimal in the worst case. For computing the maximum distance, a lower bound Ω(m + n) is proved. This bound is also shown to be best possible by establishing an upper bound of O(m + n).},
author = {Edelsbrunner, Herbert},
issn = {1090-2678},
journal = {Journal of Algorithms},
number = {2},
pages = {213 -- 224},
publisher = {Academic Press},
title = {{Computing the extreme distances between two convex polygons}},
doi = {10.1016/0196-6774(85)90039-2},
volume = {6},
year = {1985},
}