Wireless Mesh Network design by Optimization of Spectral Properties and Max-k-Cut

Topology control and channel assignment are key steps in the design of Wireless Mesh Networks (WMNs). Topology control consists of selecting a subset of communication links to set up the routing network, subject to certain degree constraints. Assigning non-overlapping frequency channels to the selected links in order to minimize the interference during communication is called the channel assignment problem. For topology control, we optimize spectral properties of the network graph such as effective resistance and second smallest eigenvalue of the graph Laplacian. We are not aware of usage of these quantities in WMN literature even though they are well-studied in other contexts. For channel assignment, we minimize total interference assuming all the links are active. Based on our simulations, we recommend methods to use depend on the network size. We further propose an alternating minimization scheme to jointly optimize topology and channel assignment and leave it for future work. DAP Committee members: Ryan Tibshirani 〈[email protected]〉 (Statistics & Machine Learning); Javier Peña 〈[email protected]〉 (Tepper School); Andrew Price 〈[email protected]〉 (A Large Internet Company) Approved by DAP Committee Chair: