  Selecting a small set of representatives from a large database is important
in many applications such as multi-criteria decision making, web search, and
recommendation. The $k$-regret minimizing set ($k$-RMS) problem was recently
proposed for representative tuple discovery. Specifically, for a large database
$P$ of tuples with multiple numerical attributes, the $k$-RMS problem returns a
size-$r$ subset $Q$ of $P$ such that, for any possible ranking function, the
score of the top-ranked tuple in $Q$ is not much worse than the score of the
$k$\textsuperscript{th}-ranked tuple in $P$. Although the $k$-RMS problem has
been extensively studied in the literature, existing methods are designed for
the static setting and cannot maintain the result efficiently when the database
is updated. To address this issue, we propose the first fully-dynamic algorithm
for the $k$-RMS problem that can efficiently provide the up-to-date result
w.r.t.~any insertion and deletion in the database with a provable guarantee.
Experimental results on several real-world and synthetic datasets demonstrate
that our algorithm runs up to four orders of magnitude faster than existing
$k$-RMS algorithms while returning results of nearly equal quality.
