Closure Solvability for Network Coding and Secret Sharing
Network coding is a new technique to transmit data through a network by letting the intermediate nodes combines the packets they receive. Given a network, the network coding solvability problem decides whether all the packets requested by the destinations can be transmitted. In this paper, the authors introduce a new approach to this problem. They define a closure operator on a digraph closely related to the network coding instance and they show that the constraints for network coding can all be expressed according to that closure operator. Thus, a solution for the network coding problem is equivalent to a so-called solution of the closure operator.