TR-96-25: On the Impact of Sense of Direction on Communication Complexity

In this paper, we prove a general result on the impact of Sense of Direction. We show that, in arbitrary graphs, any Sense of Direction has a dramatic eect on the communication complexity of several important distributed problems: Broadcast, Depth-First Traversal, Election, and Spanning Tree Construction. In systems with n nodes and e communication links, the solution for the the Depth First Traversal and the Broadcast problems require Ω(e) messages without labeling; we show that, with any Sense of Direction, they can be solved exchanging only Θ(n) messages, even if the system is anonymous. The problems of Election and of Spanning-Tree Construction require Ω(e+n log n) messages in absence of labeling; on the other hand, with Sense of Direction we show that they can be solved with Θ(n) messages.The results presented here completely explain and generalize the existing results which now follow as corollaries for specic labelings.

TR-96-25.pdf