ILP formulation for controller tree design in SDN

We consider a software defined network (SDN) with a single controller communicating with all switches through a spanning tree rooted at the controller, or a controller tree. When a switch fails, its immediate downstream switch(es) will detect the failure. A downstream switch is protected if it has a neighbor whose path to the controller is not affected by this failure. By rerouting its traffic to this neighbor, the protected switch will bypass the failure (of its parent). On the other hand, an unprotected switch cannot bypass the failure using the local rerouting above; and the subtree rooted at the unprotected switch will be disconnected from the controller. Let the weight of an unprotected switch be the number of switches in the subtree. Then the weight of a controller tree is the total weight of all unprotected switches. In this paper, we focus on the problem of finding the minimum weight controller tree (mwCT). We first introduce a new switch protection mechanism called sibling protection. We then prove that the mwCT problem is NP-hard. To solve it, we formulate the first Integer Linear Programming (ILP). We show that the solutions obtained by an existing heuristic are far from optimal.