TOPOLOGICAL CONSTRAINTS FOR SENSE OF DIRECTION

Abstract

In a distributed system, each entity has a label (port number) associated to each of its neighbors. It is well known that if the labeling satisfies a global consistency property called Sense of Direction, the communication complexity of many distributed problem can be greatly reduced. This property is assumed to be present and it is implicitly used in most interconnection networks. In this paper we investigate the nature of the relationship between Sense of Direction and network topology. We first consider the class of labelings which only satisfy the requirement of local orientation; that is, at each node, the outgoing edges have distinct labels. We then consider the class of labelings which also satisfy edge symmetry; that is, there exists a correlation between the labels neighbors give to their connecting edge. This class includes most of used labelings. We completely characterize the interplay between topological constraints and consistency constraints for these two classes of labelings. In fact, for each class, we identify both the set of forbidden subgraphs and the set of feasible graphs, and we show that the characterization is complete.