The discrete Fr'echet distance is a measure of similarity between point
sequences which permits to abstract differences of resolution between the two
curves, approximating the original Fr{'e}chet distance between curves. Such
distance between sequences of respective length $n$ and $m$ can be computed in
time within $O(nm)$ and space within $O(n+m)$ using classical dynamic
programming techniques, a complexity likely to be optimal in the worst case
over sequences of similar length unless the Strong Exponential Time Hypothesis
is proved incorrect. We propose a parameterized analysis of the computational
complexity of the discrete Fr{'e}chet distance in function of the area of the
dynamic program matrix relevant to the computation, measured by its
emph{certificate width} $omega$. We prove that the discrete Fr'echet distance
can be computed in time within $O((n+m)omega)$ and space within $O(n+m)$.