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In this paper, we propose a new approach to find a static solution for a multicast network problem. Our work relates the existence of a static network code to minimal subtree graphs of a given network. For a given multicast network there are different solutions. Sometimes some links of a network may be removed and then we will be encountered with link failure in the network. Therefore, to choose a specific satisfactory network code solution among different options, we must see how much the network code adds the network robustness against link failures. In this paper we extend the definition of the minimal subtree graph and replace it with a new definition of minimal subgraph and show that the static network code that is robust against all of solvable link failure patterns is a code that comes from solving all minimal subgraphs of a given network simultaneously.
Date of Conference: 1-3 April 2008