Submodular rate region models for multicast communication in wireless networks

Description

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. Read more... Abstract: 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 Front Matter ....Pages i-xxiii Introduction (Maximilian Riemensberger)....Pages 1-14 Submodular Information Flow Models for Multicast Communication (Maximilian Riemensberger)....Pages 15-65 Network Utility Maximization via Submodular Dual Decomposition (Maximilian Riemensberger)....Pages 67-104 Network Coding Bounds and Submodularity (Maximilian Riemensberger)....Pages 105-153 Deterministic and Linear Finite Field Networks (Maximilian Riemensberger)....Pages 155-174 Erasure Broadcast Networks (Maximilian Riemensberger)....Pages 175-203 Network Coding Bounds for Gaussian Networks (Maximilian Riemensberger)....Pages 205-246 Numerical Results for Gaussian Networks (Maximilian Riemensberger)....Pages 247-278 Concluding Remarks (Maximilian Riemensberger)....Pages 279-281