  In this addendum, we show that the switching algorithm QPS-SERENA can be
converted R(QPS-SERENA), an algorithm for computing approximate Maximum Weight
Matching (MWM). Empirically, R(QPS-SERENA) computes $(1-\epsilon)$-MWM within
linear time (with respect to the number of edges $N^2$) for any fixed
$\epsilon\in (0,1)$, for complete bipartite graphs with {\it i.i.d.} uniform
edge weight distributions. This efficacy matches that of the state-of-art
solution, although we so far cannot prove any theoretical guarantees on the
time complexities needed to attain a certain approximation ratio. Then, we have
similarly converted QPS-SERENADE to R(QPS-SERENADE), which empirically should
output $(1-\epsilon)$-MWM within only $O(N \log N)$ time for the same type of
complete bipartite graphs as described above.
