Covering Spaces, Boundary Sets, and Interconnection Networks
Michael David Rice · Annals of the New York Academy of Sciences · 1994
ABSTRACT: The paper introduces the ideas of algebraic mapping and boundary set as discrete analogues of the topological concepts of covering space mapping and boundary. These ideas are used to investigate various aspects of the theory of interconnection networks. Theorems 3 and 4 formalize and extend the discussion of group action graphs and Cayley graphs presented in [2]. Theorem 3 establishes the existence of a pair of adjoint functors between two special categories of interconnection networks. Theorem 4 characterizes the algebraic mappings with a universal lifting property. Using boundary sets, Theorems 6, 7, and 8 provide a mathematical foundation for the idea of wavefront computation discussed in [8] and [13].