On Calculating the Minimum Rate for the Cooperative Data Exchange Problem Over Fully Connected Networks

We study the cooperative data exchange problem for fully connected networks. In this problem, nodes make broadcast transmissions to recover a file consisting of
$K$
independent packets. Each node initially only possesses a subset of the packets. We propose
$(d,K)$
-Basis Searching, a deterministic polynomial-time minimization approach, to calculate the minimum rate for this problem.
$(d,K)$
-Basis Searching has strictly reduced complexity compared with the state-of-the-art algorithms, which are based on submodular function minimization. We extend our algorithm to a generalized problem: the so-called successive local omniscience problem.