Snap-Stabilization in Message-Passing Systems

In this paper, we tackle the open problem of snap-stabilization in message-passing systems. Snap-stabilization is a nice approach to design protocols that withstand transient faults. Compared to the well-known self-stabilizing approach, snap-stabilization guarantees that the effect of faults is contained immediately after faults cease to occur. Our contribution is twofold: we show that (1) snap-stabilization is impossible for a wide class of problems if we consider networks with finite yet unbounded channel capacity; (2) snap-stabilization becomes possible in the same setting if we assume bounded-capacity channels. We propose three snap-stabilizing protocols working in fully-connected networks. Our work opens exciting new research perspectives, as it enables the snap-stabilizing paradigm to be implemented in actual networks

Self-stabilizing minimum-degree spanning tree within one from the optimal degree

International audienceWe 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 ∆∗ + 1, 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 O(mn2 log n) where m is the number of edges and n is the number of nodes. The memory complexity is O(δ log n) in the send-receive atomicity model (δ is the maximal degree of the network)

Optimal Snap-Stabilizing PIF Algorithms in Un-Oriented Trees

A snap-stabilizing protocol, starting from any arbitrary initial system configuration, always behaves according to its specification. In other words, a snap-stabilizing protocol is a self-stabilizing protocol which stabilizes in zero steps. In this paper, we first prove the number of states required on processors to design a snap-stabilizing Propagation of Information with Feedback (PIF) algorithm in arbitrary un-oriented trees running under any distributed daemon (four states per processor for the middle processors and two states for each of the two extreme end processors). Then, we propose two snap-stabilizing PIF algorithms for un-oriented trees. The former works under any (fair or unfair, central or distributed) daemon. It matches the lower bound in terms of number of states we established in this paper. The latter works under any (fair or unfair) central daemon. It uses only three states for the internal processors (two states for the root and the leaves). It is optimal in terms of number of states assuming a central daemon. Thus, both algorithms are optimal both in terms of the stabilization time (zero steps) and state requirement per processor