  The compression of highly repetitive strings (i.e., strings with many
repetitions) has been a central research topic in string processing, and quite
a few compression methods for these strings have been proposed thus far. Among
them, an efficient compression format gathering increasing attention is the
run-length Burrows--Wheeler transform (RLBWT), which is a run-length encoded
BWT as a reversible permutation of an input string on the lexicographical order
of suffixes. State-of-the-art construction algorithms of RLBWT have a serious
issue with respect to (i) non-optimal computation time or (ii) a working space
that is linearly proportional to the length of an input string. In this paper,
we present \emph{r-comp}, the first optimal-time construction algorithm of
RLBWT in BWT-runs bounded space. That is, the computational complexity of
r-comp is $O(n + r \log{r})$ time and $O(r\log{n})$ bits of working space for
the length $n$ of an input string and the number $r$ of equal-letter runs in
BWT. The computation time is optimal (i.e., $O(n)$) for strings with the
property $r=O(n/\log{n})$, which holds for most highly repetitive strings.
Experiments using a real-world dataset of highly repetitive strings show the
effectiveness of r-comp with respect to computation time and space.
