Similarity of closed polygonal curves in Frechet metric

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