In a generic wireless network where the activation of a transmission link is subject to its signal-to-noise-and-interference ratio (SINR) constraint, one of the most fundamental and yet challenging problem is to find the maximum number of simultaneous transmissions. In this thesis, we consider and study in detail the problem of maximum link activation in wireless networks based on the SINR model. Integer Linear Programming has been used as the main tool in this thesis for the design of algorithms. Fast algorithms have been proposed for the delivery of near-optimal results time-efficiently. With the state-of-art Gurobi optimization solver, both the conventional approach consisting of all the SINR constraints explicitly and the exact algorithm developed recently using cutting planes have been implemented in the thesis. Based on those implementations, new solution algorithms have been proposed for the fast delivery of solutions. Instead of considering interference from all other links, an interference range has been proposed. Two scenarios have been considered, namely the optimistic case and the pessimistic case. The optimistic case considers no interference from outside the interference range, while the pessimistic case considers the interference from outside the range as a common large value. Together with the algorithms, further enhancement procedures on the data analysis have also been proposed to facilitate the computation in the solver.

An analytical framework is developed for distributed management of large networks where each node makes locally its decisions. Two issues remain open. One is whether a distributed algorithm would result in a near-optimal management. The other is the complexity, i.e., whether a distributed algorithm would scale gracefully with a network size. We study these issues through modeling, approximation, and randomized distributed algorithms. For near-optimality issue, we first derive a global probabilistic model of network management variables which characterizes the complex spatial dependence of the variables. The spatial dependence results from externally imposed management constraints and internal properties of communication environments. We then apply probabilistic graphical models in machine learning to show when and whether the global model can be approximated by a local model. This study results in a sufficient condition for distributed management to be nearly optimal. We then show how to obtain a near-optimal configuration through decentralized adaptation of local configurations. We next derive a near-optimal distributed inference algorithm based on the derived local model. We characterize the trade-off between near-optimality and complexity of distributed and statistical management. We validate our formulation and theory through simulations.