  The fine-grained complexity of computing the Fr\'echet distance has been a
topic of much recent work, starting with the quadratic SETH-based conditional
lower bound by Bringmann from 2014. Subsequent work established largely the
same complexity lower bounds for the Fr\'echet distance in 1D. However, the
imbalanced case, which was shown by Bringmann to be tight in dimensions $d\geq
2$, was still left open. Filling in this gap, we show that a faster algorithm
for the Fr\'echet distance in the imbalanced case is possible: Given two
1-dimensional curves of complexity $n$ and $n^{\alpha}$ for some $\alpha \in
(0,1)$, we can compute their Fr\'echet distance in $O(n^{2\alpha} \log^2 n + n
\log n)$ time. This rules out a conditional lower bound of the form
$O((nm)^{1-\epsilon})$ that Bringmann showed for $d \geq 2$ and any
$\varepsilon>0$ in turn showing a strict separation with the setting $d=1$. At
the heart of our approach lies a data structure that stores a 1-dimensional
curve $P$ of complexity $n$, and supports queries with a curve $Q$ of
complexity~$m$ for the continuous Fr\'echet distance between $P$ and $Q$. The
data structure has size in $\mathcal{O}(n\log n)$ and uses query time in
$\mathcal{O}(m^2 \log^2 n)$. Our proof uses a key lemma that is based on the
concept of visiting orders and may be of independent interest. We demonstrate
this by substantially simplifying the correctness proof of a clustering
algorithm by Driemel, Krivo\v{s}ija and Sohler from 2015.
