On the Problem of Optimal Path Encoding for Software-Defined Networks

Packet networks need to maintain the state in the form of forwarding tables at each switch. The cost of this state increases as networks support ever more sophisticated per-flow routing, traffic engineering, and service chaining. Per-flow or per-path state at the switches can be eliminated by encoding each packet’s desired path in its header. A key component of such a method is an efficient encoding of paths through the network. We introduce a mathematical formulation of this optimal path-encoding problem. We prove that the problem is APX-hard, by showing that approximating it to within a factor less than $8/7$ is NP-hard. Thus, at best, we can hope for a constant-factor approximation algorithm. We then present such an algorithm, approximating the optimal path-encoding problem to within a factor 2. Finally, we provide the empirical results illustrating the effectiveness of the proposed algorithm.