Complexity and Algorithms for the Discrete Fréchet Distance Upper Bound with Imprecise Input

We study the problem of computing the upper bound of the discrete Fréchet distance for imprecise input, and prove that the problem is NP-hard. This solves an open problem posed in 2010 by Ahn \emph{et al}. If shortcuts are allowed, we show that the upper bound of the discrete Fréchet distance with shortcuts for imprecise input can be computed in polynomial time and we present several efficient algorithms.