  Distributed configuration management is imperative for wireless
infrastructureless networks where each node adjusts locally its physical and
logical configuration through information exchange with neighbors. Two issues
remain open. The first is the optimality. The second is the complexity. We
study these issues through modeling, analysis, and randomized distributed
algorithms. Modeling defines the optimality. We first derive a global
probabilistic model for a network configuration which characterizes jointly the
statistical spatial dependence of a physical- and a logical-configuration. We
then show that a local model which approximates the global model is a two-layer
Markov Random Field or a random bond model. The complexity of the local model
is the communication range among nodes. The local model is near-optimal when
the approximation error to the global model is within a given error bound. We
analyze the trade-off between an approximation error and complexity, and derive
sufficient conditions on the near-optimality of the local model. We validate
the model, the analysis and the randomized distributed algorithms also through
simulation.
