  In distributed wireless networks, nodes often do not know the topology
(network size, connectivity and the channel gains) of the network. Thus, they
have to compute their transmission and reception parameters in a distributed
fashion. In this paper, we consider that each of the transmitter know the
channel gains of all the links that are at-most two-hop distant from it and the
receiver knows the channel gains of all the links that are three-hop distant
from it in a deterministic interference channel. With this limited information,
we find a condition on the network connectivity for which there exist a
distributed strategy that can be chosen by the users with partial information
about the network state, which achieves the same sum capacity as that
achievable by the centralized server that knows all the channel gains.
Specifically, distributed decisions are sum-rate optimal only if each connected
component is in a one-to-many configuration or a fully-connected configuration.
In all other cases of network connectivity, the loss can be arbitrarily large.
