In the field of optical interferometry, two-dimensional projections of light interference patterns are often analysed in order to obtain measurements of interest. Such interference patterns, or interferograms, contain phase information which is inherently wrapped onto the range -t to it. Phase unwrapping is the processes of the restoration of the unknown multiple of 2ir, and therefore plays a major role in the overall process of interferogram analysis. Unwrapping phase information correctly becomes a challenging process in the presence of noise. This is particularly the case for speckle interferograms, which are noisy by nature. Many phase unwrapping algorithms have been devised by workers in the field, in order to achieve better noise rejection and improve the computational performance. This thesis focuses on the computational efficiency aspect, and picks as a starting point an existing phase unwrapping algorithm which has been shown to have inherent noise immunity. This is, namely, the tile-based phase unwrapping method, which attains its enhanced noise immunity through the application of the minimum spanning tree concept from graph theory. The thesis examines the problem of finding a minimum spanning tree, for this particular application, from a graph theory perspective, and shows that a more efficient class of minimum spanning tree algorithms can be applied to the problem. The thesis then goes on to show how a novel algorithm can be used to significantly reduce the size of the minimum spanning tree problem in an efficient manner.