On the Feasibility of Precoding-Based Network Alignment for Three Unicast Sessions
The authors consider the problem of network coding across three uni-cast sessions over a directed acyclic graph, when each session has min-cut one. In this paper, they first prove that the set of conditions provided by Das-Et al are also necessary for the feasibility of PBNA with respect to any pre-coding matrix. Then, using two graph-related properties and a degree-counting technique, they reduce the set to just four conditions. This reduction enables an efficient algorithm for checking the feasibility of PBNA on a given graph.