  The Fr\'{e}chet distance is a well studied and commonly used measure to
capture the similarity of polygonal curves. Unfortunately, it exhibits a high
sensitivity to the presence of outliers. Since the presence of outliers is a
frequently occurring phenomenon in practice, a robust variant of Fr\'{e}chet
distance is required which absorbs outliers. We study such a variant here. In
this modified variant, our objective is to minimize the length of subcurves of
two polygonal curves that need to be ignored (MinEx problem), or alternately,
maximize the length of subcurves that are preserved (MaxIn problem), to achieve
a given Fr\'{e}chet distance. An exact solution to one problem would imply an
exact solution to the other problem. However, we show that these problems are
not solvable by radicals over $\mathbb{Q}$ and that the degree of the
polynomial equations involved is unbounded in general. This motivates the
search for approximate solutions. We present an algorithm, which approximates,
for a given input parameter $\delta$, optimal solutions for the \MinEx\ and
\MaxIn\ problems up to an additive approximation error $\delta$ times the
length of the input curves. The resulting running time is upper bounded by
$\mathcal{O} \left(\frac{n^3}{\delta} \log \left(\frac{n}{\delta}
\right)\right)$, where $n$ is the complexity of the input polygonal curves.
