Given a point set S and a polygonal curve P in R, we study the problem of finding a polygonal curve through S, which has a minimum Fréchet distance to P . We present an efficient algorithm to solve the decision version of this problem in O(nk) time, where n and k represent the sizes of P and S, respectively. A curve minimizing the Fréchet distance can be computed in O(nk log(nk)) time. As a by-...