This thesis explores the PMU placement problem, that is, the placement of a minimal number of Phase Measurement Units (PMUs) on the nodes of a power system graph such that the entire graph is observed. The NP-completeness of PMU placement for planar bipartite graphs is shown. PMU placement algorithms are developed for graphs of bounded tree width, such as trees and outer planar graphs. Graph decompositions are used to develop efficient algorithms that produce minimal PMU covers. These algorithms are developed, analyzed, and compared theoretically. Algorithm animations were used in the study to develop insight into the problem and to understand algorithm behavior. / Master of Science