Self-stabilizing network orientation algorithms in arbitrary rooted networks

Network orientation is the problem of assigning different labels to the edges at each processor, in a globally consistent manner. A self-stabilizing protocol guarantees that the system will arrive at a legitimate state in finite time, irrespective of the initial state of the system. Two deterministic distributed network orientation protocols on arbitrary rooted, asynchronous networks are proposed in this work. Both protocols set up a chordal sense of direction in the network. The protocols are self-stabilizing, meaning that starting from an arbitrary state, the protocols are guaranteed to reach a state in which every processor has a valid node label and every link has a valid edge label. The first protocol assumes an underlying depth-first token circulation protocol; it orients the network as the token is passed among the nodes and stabilizes in O(n) steps after the token circulation stabilizes, where n is the number of processors in the network. The second protocol is designed on an underlying spanning tree protocol and stabilizes in O(h) time, after the spanning tree is constructed, where h is the height of the spanning tree. Although the second protocol assumes the existence of a spanning tree of the rooted network, it orients all edges--both tree and non-tree edges--of the network

Silent Self-stabilizing BFS Tree Algorithms Revised

In this paper, we revisit two fundamental results of the self-stabilizing literature about silent BFS spanning tree constructions: the Dolev et al algorithm and the Huang and Chen's algorithm. More precisely, we propose in the composite atomicity model three straightforward adaptations inspired from those algorithms. We then present a deep study of these three algorithms. Our results are related to both correctness (convergence and closure, assuming a distributed unfair daemon) and complexity (analysis of the stabilization time in terms of rounds and steps)

Self-Stabilization in the Distributed Systems of Finite State Machines

The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems