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Given a boolean predicate Π on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for Π is a distributed algorithm that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each of its variables), and eventually converge to a configuration satisfying Π. It is known that leader election does not have a deterministic self-stabilizing algorithm using a constant-size register at each node, i.e., for some networks, some of their nodes must have registers whose sizes grow with the size n of the networks. On the other hand, it is also known that leader election can be solved by a deterministic self-stabilizing algorithm using registers of O(log log n) bits per node in any n-node bounded-degree network. We show that this latter space complexity is optimal. Specifically, we prove that every deterministic self-stabilizing algorithm solving leader election must use (log log n)-bit per node registers in some n-node networks. In addition, we show that our lower bounds go beyond leader election, and apply to all problems that cannot be solved by anonymous algorithms. [ABSTRACT FROM AUTHOR]

Routing protocols are at the core of distributed systems performances, especially in the presence of faults. A classical approach to this problem is to build a spanning tree of the distributed system. Numerous spanning tree construction algorithms depending on the optimized metric exist (total weight, height, distance with respect to a particular process, …) both in fault-free and faulty environments. In this paper, we aim at optimizing the diameter of the spanning tree by constructing a minimum diameter spanning tree. We target environments subject to transient faults ( i.e. faults of finite duration). Hence, we present a self-stabilizing algorithm for the minimum diameter spanning tree construction problem in the state model. Our protocol has the following attractive features. It is the first algorithm for this problem that operates under the unfair and distributed adversary (or daemon ). In other words, no restriction is made on the asynchronous behavior of the system. Second, our algorithm needs only O ( log n ) bits of memory per process (where n is the number of processes), that improves the previous result by a factor n . These features are not achieved to the detriment of the convergence time, which stays polynomial. [ABSTRACT FROM AUTHOR]

The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol.We present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Secondly, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date. [ABSTRACT FROM AUTHOR]

Abstract: We propose a self-stabilizing algorithm for constructing a Minimum Degree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most , where is the minimum possible maximum degree of a spanning tree of the network. To the best of our knowledge, our algorithm is the first self-stabilizing solution for the construction of a minimum degree spanning tree in undirected graphs. The algorithm uses only local communications (nodes interact only with the neighbors at one hop distance). Moreover, the algorithm is designed to work in any asynchronous message passing network with reliable FIFO channels. Additionally, we use a fine grained atomicity model (i.e., the send/receive atomicity). The time complexity of our solution is where is the number of edges and is the number of nodes. The memory complexity is in the send–receive atomicity model ( is the maximal degree of the network). [ABSTRACT FROM AUTHOR]