Finding the minimum vertex distance between two disjoint convex polygons in linear time (Q1071519)

Let \(V=\{v_ 1,v_ 2,...,v_ m\}\) and \(W=\{w_ 1,w_ 2,...,w_ n\}\) be two linearly separable convex polygons whose vertices are specified by their Cartesian coordinates in order. An algorithm with \(O(m+n)\) worst- case time complexity is described for finding the minimum Euclidean distance between a vertex \(v_ 1\) in V and a vertex \(w_ j\) in W. It is also shown that the algorithm is optimal.