  For a large multi-hop wireless network, nodes are preferable to make
distributed and localized link-scheduling decisions with only interactions
among a small number of neighbors. However, for a slowly decaying channel and
densely populated interferers, a small size neighborhood often results in
nontrivial link outages and is thus insufficient for making optimal scheduling
decisions. A question arises how to deal with the information outside a
neighborhood in distributed link-scheduling. In this work, we develop joint
approximation of information and distributed link scheduling. We first apply
machine learning approaches to model distributed link-scheduling with complete
information. We then characterize the information outside a neighborhood in
form of residual interference as a random loss variable. The loss variable is
further characterized by either a Mean Field approximation or a normal
distribution based on the Lyapunov central limit theorem. The approximated
information outside a neighborhood is incorporated in a factor graph. This
results in joint approximation and distributed link-scheduling in an iterative
fashion. Link-scheduling decisions are first made at each individual node based
on the approximated loss variables. Loss variables are then updated and used
for next link-scheduling decisions. The algorithm repeats between these two
phases until convergence. Interactive iterations among these variables are
implemented with a message-passing algorithm over a factor graph. Simulation
results show that using learned information outside a neighborhood jointly with
distributed link-scheduling reduces the outage probability close to zero even
for a small neighborhood.
