  The prevalent technique for DNA sequencing consists of two main steps:
shotgun sequencing, where many randomly located fragments, called reads, are
extracted from the overall sequence, followed by an assembly algorithm that
aims to reconstruct the original sequence. There are many different
technologies that generate the reads: widely-used second-generation methods
create short reads with low error rates, while emerging third-generation
methods create long reads with high error rates. Both error rates and error
profiles differ among methods, so reconstruction algorithms are often tailored
to specific shotgun sequencing technologies. As these methods change over time,
a fundamental question is whether there exist reconstruction algorithms which
are robust, i.e., which perform well under a wide range of error distributions.
  Here we study this question of sequence assembly from corrupted reads. We
make no assumption on the types of errors in the reads, but only assume a bound
on their magnitude. More precisely, for each read we assume that instead of
receiving the true read with no errors, we receive a corrupted read which has
edit distance at most $\epsilon$ times the length of the read from the true
read. We show that if the reads are long enough and there are sufficiently many
of them, then approximate reconstruction is possible: we construct a simple
algorithm such that for almost all original sequences the output of the
algorithm is a sequence whose edit distance from the original one is at most
$O(\epsilon)$ times the length of the original sequence.
