In this paper, we prove a general result on the impact of sense of dir
ection, We show that, in arbitrary graphs, any sense of direction has
a dramatic effect 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 communicati
on links, the solution for the Depth First Traversal and the Broadcast
problems require Omega(e) messages with arbitrary labelings; we show
that, with any sense of direction, they can be solved exchanging only
Theta(n) messages, even if the system is anonymous. The problems of El
ection and of Spanning Tree Construction require Omega(e + n log n) me
ssages with arbitrary labelings; on the other hand, we show that they
can be solved with Theta(n) messages with any sense of direction. The
results presented here completely explain and generalize the existing
results which now follow as corollaries for specific labelings. (C) 19
97 Elsevier Science B.V.