  We study the classic online bipartite matching problem with a twist: offline
vertices, called resources, are $\textit{reusable}$. In particular, when a
resource is matched to an online vertex it is unavailable for a deterministic
time duration $d$ after which it becomes available again for a re-match. Thus,
a resource can be matched to many different online vertices over a period of
time. While recent work on the problem have resolved the asymptotic case where
we have large starting inventory (i.e., many copies) of every resource, we
consider the (more general) case of $\textit{unit inventory}$ and give the
first algorithms that are provably better than the naive greedy approach which
has a competitive ratio of (exactly) 0.5. Our first algorithm, which achieves a
competitive ratio of $0.589$, generalizes the classic RANKING algorithm for
online bipartite matching of non-reusable resources (Karp et al., 1990), by
$\textit{reranking}$ resources independently over time. While reranking
resources frequently has the same worst case performance as greedy, we show
that reranking intermittently on a periodic schedule succeeds in addressing
reusability of resources and performs significantly better than greedy in the
worst case. Our second algorithm, which achieves a competitive ratio of
$0.505$, is a primal-dual randomized algorithm that works by suggesting up to
two resources as candidate matches for every online vertex, and then breaking
the tie to make the final matching selection in a randomized correlated fashion
over time. As a key component of our algorithm, we suitably adapt and extend
the powerful technique of online correlated selection (Fahrbach et al., 2020)
to reusable resources, in order to induce negative correlation in our tie
breaking step and to beat the competitive ratio of $0.5$. Both of our results
also extend to the case where offline vertices have weights.
