Static network codes using network minimal subgraphs

For a given multicast network problem, there are different solutions. Sometimes some links of a network may be removed by failure and then we will be encountered with link failure in the network. Therefore, one of the objectives of selecting a specific network code solution among different options is to increase the robustness provided by this solution against such failure. In this paper we extend the definition of the minimal subtree graph and replace it with a new definition of minimal subgraph and use it as a basis of a faster method with lower complexity for finding a static network code resistant against all solvable link failure patterns of a network.