  The problem of computing a bi-Lipschitz embedding of a graphical metric into
the line with minimum distortion has received a lot of attention. The
best-known approximation algorithm computes an embedding with distortion
$O(c^2)$, where $c$ denotes the optimal distortion [B\u{a}doiu \etal~2005]. We
present a bi-criteria approximation algorithm that extends the above results to
the setting of \emph{outliers}.
  Specifically, we say that a metric space $(X,\rho)$ admits a
$(k,c)$-embedding if there exists $K\subset X$, with $|K|=k$, such that
$(X\setminus K, \rho)$ admits an embedding into the line with distortion at
most $c$. Given $k\geq 0$, and a metric space that admits a $(k,c)$-embedding,
for some $c\geq 1$, our algorithm computes a $({\mathsf p}{\mathsf o}{\mathsf
l}{\mathsf y}(k, c, \log n), {\mathsf p}{\mathsf o}{\mathsf l}{\mathsf
y}(c))$-embedding in polynomial time. This is the first algorithmic result for
outlier bi-Lipschitz embeddings. Prior to our work, comparable outlier
embeddings where known only for the case of additive distortion.
