  In the query-commit problem we are given a graph where edges have distinct
probabilities of existing. It is possible to query the edges of the graph, and
if the queried edge exists then its endpoints are irrevocably matched. The goal
is to find a querying strategy which maximizes the expected size of the
matching obtained. This stochastic matching setup is motivated by applications
in kidney exchanges and online dating.
  In this paper we address the query-commit problem from both theoretical and
experimental perspectives. First, we show that a simple class of edges can be
queried without compromising the optimality of the strategy. This property is
then used to obtain in polynomial time an optimal querying strategy when the
input graph is sparse. Next we turn our attentions to the kidney exchange
application, focusing on instances modeled over real data from existing
exchange programs. We prove that, as the number of nodes grows, almost every
instance admits a strategy which matches almost all nodes. This result supports
the intuition that more exchanges are possible on a larger pool of
patient/donors and gives theoretical justification for unifying the existing
exchange programs. Finally, we evaluate experimentally different querying
strategies over kidney exchange instances. We show that even very simple
heuristics perform fairly well, being within 1.5% of an optimal clairvoyant
strategy, that knows in advance the edges in the graph. In such a
time-sensitive application, this result motivates the use of committing
strategies.
