On achieving optimal throughput with network coding

With the constraints of network topologies and link capacities, achieving the optimal end-to-end throughput in data networks has been known as a fundamental but computationally hard problem. In this paper, we seek efficient solutions to the problem of achieving optimal throughput in data networks, with single or multiple unicast, multicast and broadcast sessions. Although previous approaches lead to solving NP-complete problems, we show the surprising result that, facilitated by the recent advances of network coding, computing the strategies to achieve the optimal end-to-end throughput can be performed in polynomial time. This result holds for one or more communication sessions, as well as in the overlay network model. Supported by empirical studies, we present the surprising observation that in most topologies, applying network coding may not improve the achievable optimal throughput; rather, it facilitates the design of significantly more efficient algorithms to achieve such optimality.