  In the trace reconstruction problem, the goal is to reconstruct an unknown
string $x$ of length $n$ from multiple traces obtained by passing $x$ through
the deletion channel. In the relaxed problem of $approximate$ trace
reconstruction, the goal is to reconstruct an approximation $\widehat{x}$ of
$x$ which is close (within $\epsilon n$) to $x$ in edit distance. We show that
for most strings $x$, this is possible with high probability using only a
constant number of traces. Crucially, this constant does not grow with $n$, and
only depends on the deletion probability and $\epsilon$.
