  $k$-Approximate distance labeling schemes are schemes that label the vertices
of a graph with short labels in such a way that the $k$-approximation of the
distance between any two vertices $u$ and $v$ can be determined efficiently by
merely inspecting the labels of $u$ and $v$, without using any other
information. One of the important problems is finding natural classes of graphs
admitting exact or approximate distance labeling schemes with labels of
polylogarithmic size. In this paper, we describe a $4$-approximate distance
labeling scheme forthe class of $K_4$-free bridged graphs. This scheme uses
labels of poly-logarithmic length $O(\log n^3)$ allowing a constant decoding
time. Given the labels of two vertices $u$ and $v$, the decoding function
returnsa value between the exact distance $d_G(u,v)$ and its quadruple
$4d_G(u,v)$.
