  In this paper we describe algorithms for computing the BWT and for building
(compressed) indexes in external memory. The innovative feature of our
algorithms is that they are lightweight in the sense that, for an input of size
$n$, they use only ${n}$ bits of disk working space while all previous
approaches use $\Th{n \log n}$ bits of disk working space. Moreover, our
algorithms access disk data only via sequential scans, thus they take full
advantage of modern disk features that make sequential disk accesses much
faster than random accesses.
  We also present a scan-based algorithm for inverting the BWT that uses
$\Th{n}$ bits of working space, and a lightweight {\em internal-memory}
algorithm for computing the BWT which is the fastest in the literature when the
available working space is $\os{n}$ bits.
  Finally, we prove {\em lower} bounds on the complexity of computing and
inverting the BWT via sequential scans in terms of the classic product:
internal-memory space $\times$ number of passes over the disk data.
