Network Coding for Speedup in Switches

We present a graph theoretic upper bound on speedup needed to achieve 100% throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches - i.e. network coding, which is usually implemented using software, can in many cases substitute speedup, which is often achieved by adding extra switch fabrics. This bound is based on an approach to network coding problems called the "enhanced conflict graph". We show that the "imperfection ratio" of the enhanced conflict graph gives an upper bound on speedup. In particular, we apply this result to K-by-N switches with traffic patterns consisting of unicasts and broadcasts only to obtain an upper bound of min{(2K-1)/K, 2N/(N+1)}.