On the Switching Gap of Ahlswede-Cai-Li-Yeung´s Single-Source Multicast Network

Ahlswede, Cai, Li, and Yeung have proposed a new paradigm of network coding in multicast networks. They demonstrated that network coding can achieve the maximum information flow in the single-source multicast networks beyond the conventional network switching. A basic problem arising here is that, for a given single-source multicast network, what is the switching gap of the network defined as the ratio of the maximum information flow in the multicast network with network coding to that only with network switching. In this brief, we investigate the maximum possible switching gap of Ahlswede-Cai-Li-Yeung´s single-source multicast network and find some condition, in terms of the capacity of links, under which Ahlswede-Cai-Li-Yeung´s network has the minimum possible switching gap of one