We consider identified directed networks where processes know an upper bound on the maximum ancestor distance. Under these settings, we study the conditions on the network topology allowing the self-stabilization of two fundamental problems: the leader election and the synchronous unison. We show that those two problems can be self-stabilizingly solved in our settings if and only if the network contains a unique source component. In particular, to show that our condition is sufficient, we propose two algorithms and study their complexity. Notice that our topological condition covers a wide spectrum of digraphs since, for example, strongly connected digraphs, dipaths, and out-trees have a unique source component.

Self-stabilization is a general paradigm that characterizes the ability of a distributed system to recover from transient faults. Since its introduction by Dijkstra in 1974, self-stabilization has been successfully applied to efficiently solve many networking tasks. However, most of the literature focuses on bidirectional networks. Now, in today's networks such as WSNs, some communication channels may be one-way only. Considering such network topologies, a.k.a. directed graphs, makes self-stabilization more complicated, and sometimes even impossible. In this paper, we investigate the gap in terms of requirements and efficiency when considering a directed graph instead of an undirected one as network topology for a self-stabilizing algorithm. Our case study is a variant of a synchronous unison algorithm proposed by Arora et al.; the synchronous unison being a clock synchronization problem.