How local can a node´s view be and still guarantee sum-capacity in interference networks?

We study the relationship between locality of node channel state knowledge and the percent of sum-capacity achievable in partially connected K-user interference channels. In the process we 1) settle a previous conjecture regarding 3-user interference channels, 2) establish the exact number of hops of knowledge necessary and sufficient to guarantee achievability of capacity given full channel state knowledge, and 3) present an upper bounds on the normalized capacity of K-user interference networks with L-hops of knowledge and arbitrary topology.