Similarity of closed polygonal curves in Frechet metric
  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 is described. The described algorithm takes O(mn) time whereas the previously known algorithms take O(mn log(mn)) time. 
M.I. Schlesinger, E.V. Vodolazskiy, V.M. Yakovenko
cs.CG