This thesis provides three main contributions with respect to the Dynamic Channel and Power Assignment (DCPA) problem. DCPA refers to the allocation of transmit power and frequency channels to links in a cognitive dynamic spectrum network so as to maximize the total number of feasible links while minimizing the aggregate transmit power. In order to provide a method to compare related, yet disparate, work, the first contribution of this thesis is a unifying optimization formulation to describe the DCPA problem. This optimization problem is based on maximizing the number of feasible links and minimizing transmit power of a set of communications links in a given communications network. Using this optimization formulation, this thesis develops its second contribution: a evaluation method for comparing DCPA algorithms. The evaluation method is applied to five DPCA algorithms representative of the DCPA literature . These five algorithms are selected to illustrate the tradeoffs between control modes (centralized versus distributed) and channel/power assignment techniques. Initial algorithm comparisons are done by analyzing channel and power assignment techniques and algorithmic complexity of five different DCPA algorithms. Through simulations, algorithm performance is evaluated by the metrics of feasibility ratio and average power per link. Results show that the centralized algorithm Minimum Power Increase Assignment (MPIA) has the overall best feasibility ratio and the lowest average power per link of the five algorithms we investigated. Through assignment by the least change in transmit power, MPIA minimizes interference and increases the number of feasible links. However, implementation of this algorithm requires calculating the inverse of near singular matrices, which could lead to inaccurate results. The third contribution of this thesis is a proposed distributed channel assignment algorithm, Least Interfering Channel and Iterative Power Assignment (LICIPA). This distributed algorithm has the best feasibility ratio and lowest average power per link of the distributed algorithms. In some cases, LICIPA achieves 90% of the feasibility ratio of MPIA, while having lower complexity and overall lower average run time.