This book proposes representations of multicast rate regions in wireless networks based on the mathematical concept of submodular functions, e.g., the submodular cut model and the polymatroid broadcast model. These models subsume and generalize the graph and hypergraph models. The submodular structure facilitates a dual decomposition approach to network utility maximization problems, which exploits the greedy algorithm for linear programming on submodular polyhedra. This approach yields computationally efficient characterizations of inner and outer bounds on the multicast capacity regions for various classes of wireless networks.
Introduction.- Submodular Information Flow Models for Multicast Communication.- Network Utility Maximization via Submodular Dual Decomposition.- Network Coding Bounds and Submodularity.- Deterministic and Linear Finite Field Networks.- Erasure Broadcast Networks.- Network Coding Bounds for Gaussian Networks.- Numerical Results for Gaussian Networks.- Concluding Remarks.