  Multiple TSP ($\mathrm{mTSP}$) is a important variant of $\mathrm{TSP}$ where
a set of $k$ salesperson together visit a set of $n$ cities. The
$\mathrm{mTSP}$ problem has applications to many real life applications such as
vehicle routing. Rothkopf introduced another variant of $\mathrm{TSP}$ called
many-visits TSP ($\mathrm{MV\mbox{-}TSP}$) where a request $r(v)\in
\mathbb{Z}_+$ is given for each city $v$ and a single salesperson needs to
visit each city $r(v)$ times and return back to his starting point. A
combination of $\mathrm{mTSP}$ and $\mathrm{MV\mbox{-}TSP}$ called many-visits
multiple TSP $(\mathrm{MV\mbox{-}mTSP})$ was studied by B\'erczi, Mnich, and
Vincze where the authors give approximation algorithms for various variants of
$\mathrm{MV\mbox{-}mTSP}$.
  In this work, we show a simple linear programming (LP) based reduction that
converts a $\mathrm{mTSP}$ LP-based algorithm to a LP-based algorithm for
$\mathrm{MV\mbox{-}mTSP}$ with the same approximation factor. We apply this
reduction to improve or match the current best approximation factors of several
variants of the $\mathrm{MV\mbox{-}mTSP}$. Our reduction shows that the
addition of visit requests $r(v)$ to $\mathrm{mTSP}$ does $\textit{not}$ make
the problem harder to approximate even when $r(v)$ is exponential in number of
vertices.
  To apply our reduction, we either use existing LP-based algorithms for
$\mathrm{mTSP}$ variants or show that several existing combinatorial algorithms
for $\mathrm{mTSP}$ variants can be interpreted as LP-based algorithms. This
allows us to apply our reduction to these combinatorial algorithms as well
achieving the improved guarantees.
