Frechet similarity of closed polygonal curves

The article analyzes similarity of closed polygonal curves with respect to the Frechet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm is described that determines whether the Frechet distance between two closed polygonal curves with m and n vertices is less than a given number. The algorithm takes O(mn) time whereas the previously known algorithms take O(mn log(mn)) time.