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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. • We address self-stabilization of dynamic problems in anonymous directed networks. • We propose a topology-related necessary condition to solve synchronous unison in directed networks. • We present a simple self-stabilizing synchronous unison algorithm for directed networks. • We study conditions under which the proposed algorithm is self-stabilizing, and at what cost. [ABSTRACT FROM AUTHOR]

To solve reachability is to determine whether there is a path from one vertex to the other in a graph. Standard graph traversal algorithms such as DFS and BFS take linear time to solve reachability; however, their space complexity is also linear. On the other hand, Savitch's algorithm takes quasipolynomial time, although the space-bound is O (log 2 ⁡ n). In this paper, we study space-efficient algorithms for deciding reachability that runs in polynomial time. We show a polynomial-time algorithm that solves reachability in directed graphs using O (w log ⁡ n) space. Our algorithm requires access to a tree decomposition of width w for the underlying undirected graph of the input. This requirement can be waived for graphs for which recursive balanced vertex separators can be computed space-efficiently. [ABSTRACT FROM AUTHOR]