  This paper considers how to accurately estimate the minimum sum-rate so as to
reduce the complexity of solving cooperative data exchange (CDE) problems. The
CDE system contains a number of geographically close clients who send packets
to help the others recover an entire packet set. The minimum sum-rate is the
minimum value of total number of transmissions that achieves universal recovery
(the situation when all the clients recover the whole packet set). Based on a
necessary and sufficient condition for a supermodular base polyhedron to be
nonempty, we show that the minimum sum-rate for a CDE system can be determined
by a maximization over all possible partitions of the client set. Due to the
high complexity of solving this maximization problem, we propose a
deterministic algorithm to approximate a lower bound on the minimum sum-rate.
We show by experiments that this lower bound is much tighter than those lower
bounds derived in the existing literature. We also show that the deterministic
algorithm prevents from repetitively running the existing algorithms for
solving CDE problems so that the overall complexity can be reduced accordingly.
