This Research Planning Grant has as a goal the investigation of algorithmic and graph theoretic properties of hierarchical distributed systems; i.e., systems with underlying tree architectures. A major part of this study is based on a novel and universal technique for finding optimal hierarchical communication systems, applicable to different computational models. This method is based on a general purpose algorithm which efficiently generates and examines all topologically equivalent trees of a given order to find a hierarchy which minimizes a given criterion. The algorithm is efficient and general in the sense that very few restrictions are placed on the system model and the performance criteria to be examined. Several models are analyzed using the above technique first, and their further properties such as complexities and optimalities are studied. The models of hierarchical distributed systems are to be provided by Dr. Dorota M. Huizinga, California State University at Fullerton. The PI has a mentoring arrangement with Professor Steve Hedetniemi, Clemson University.
