The WiMAX technology and cognitive radio have been active topics in wireless networks. A WiMAX mesh network is able to provide larger wireless coverage, higher network capacity and Non-Line-Of-Sight (NLOS) communications. Cognitive radios enable dynamic spectrum access over a large frequency range. These characteristics make WiMAX mesh networks and cognitive radio networks able to provide users with low-cost, high-speed and long-range wireless communications, as well as better Quality of Service. However, there are still several challenges and problems to be solved in this area, such as relay station placement problems and scheduling problems. In this thesis, I studied a distance-aware relay placement problem and max-min fair scheduling problem in WiMAX mesh networks. To solve these problems, approximation algorithms and heuristic algorithms are proposed. Theoretical analysis and simulation results are provided to evaluate the solutions. I also studied a scheduling problem adopting the idea of cognitive radio technique in wireless networks over water. Two heuristics are presented to solve this unique problem. I provide the numerical results to justify the performance and efficiency of our proposed scheduling algorithms.