Two snap-stabilizing point-to-point communication protocols in message-switched networks

A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we present a snap-stabilizing protocol to solve the message forwarding problem in a message-switched network. In this problem, we must manage resources of the system to deliver messages to any processor of the network. In this purpose, we use information given by a routing algorithm. By the context of stabilization (in particular, the system starts in an arbitrary configuration), this information can be corrupted. So, the existence of a snap-stabilizing protocol for the message forwarding problem implies that we can ask the system to begin forwarding messages even if routing information are initially corrupted. In this paper, we propose two snap-stabilizing algorithms (in the state model) for the following specification of the problem: - Any message can be generated in a finite time. - Any emitted message is delivered to its destination once and only once in a finite time. This implies that our protocol can deliver any emitted message regardless of the state of routing tables in the initial configuration. These two algorithms are based on the previous work of [MS78]. Each algorithm needs a particular method to be transform into a snap-stabilizing one but both of them do not introduce a significant overcost in memory or in time with respect to algorithms of [MS78]

Stabilizing data-link over non-FIFO channels with optimal fault-resilience

Self-stabilizing systems have the ability to converge to a correct behavior when started in any configuration. Most of the work done so far in the self-stabilization area assumed either communication via shared memory or via FIFO channels. This paper is the first to lay the bases for the design of self-stabilizing message passing algorithms over unreliable non-FIFO channels. We propose a fault-send-deliver optimal stabilizing data-link layer that emulates a reliable FIFO communication channel over unreliable capacity bounded non-FIFO channels

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

Acheminement de messages instantanément stabilisant pour arbres couvrants

International audienceNous présentons un protocole instantanément stabilisant d'acheminement de messages au sein de structures couvrantes arborescentes de réseaux. Notre protocole utilise l'information fournie par un algorithme de calcul de tables de routage auto-stabilisant s'appuyant sur cette structure. Le fait que le protocole soit instantanément stabilisant signifie que tout message émis après les fautes est acheminé à son destinataire, y compris lorsque les tables de routage ne sont pas stabilisées. Notre algorithme présente l'avantage que le nombre de tampons est indépendant de tout paramètre global du réseau comme le nombre de noeuds ou le diamètre. En effet, nous montrons que le problème peut être résolu en utilisant un nombre constant de tampons par lien de communication de la structure couvrante. Cette propriété lui confère l'avantage de tolérer le passage à l'échelle

Snap-Stabilizing Message Forwarding Algorithm on Tree Topologies

In this paper, we consider the message forwarding problem that consists in managing the network resources that are used to forward messages. Previous works on this problem provide solutions that either use a significant number of buffers (that is n buffers per processor, where n is the number of processors in the network) making the solution not scalable or, they reserve all the buffers from the sender to the receiver to forward only one message %while using D buffers (where D refers to the diameter of the network) . The only solution that uses a constant number of buffers per link was introduced in [1]. However the solution works only on a chain networks. In this paper, we propose a snap-stabilizing algorithm for the message forwarding problem that uses the same complexity on the number of buffers as [1] and works on tree topologies.Nous considérons dans ce papier le problème d'acheminement de messages qui consiste à gérer les ressources du réseau. Des Solutions ont été proposées, soit qui utilisent un nombre significatif de buffers (n buffers par processeur où n correspond au nombre de processeurs dans le réseau), ce qui rend cette solution non adaptée au réseaux à grande échelle. Soit elles doivent réserver tout les buffers de la source à la destination. La seule solution qui utilise un nombre constant de buffers par lien a été introduite dans [1], cela dit cette solution fonctionne seulement sur des topologies linéaires. Dans ce papier, nous proposons un algorithme instantanément stabilisant pour le problème d'acheminement de messages ayant la même complexité en terme de nombre de buffers que [1] et qui fonctionne sur des topologies en arbre

Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction

Motivated by applications to sensor networks, as well as to many other areas, this paper studies the construction of minimum-degree spanning trees. We consider the classical node-register state model, with a weakly fair scheduler, and we present a space-optimal \emph{silent} self-stabilizing construction of minimum-degree spanning trees in this model. Computing a spanning tree with minimum degree is NP-hard. Therefore, we actually focus on constructing a spanning tree whose degree is within one from the optimal. Our algorithm uses registers on $O(\log n)$ bits, converges in a polynomial number of rounds, and performs polynomial-time computation at each node. Specifically, the algorithm constructs and stabilizes on a special class of spanning trees, with degree at most $OPT+1$. Indeed, we prove that, unless NP $=$ coNP, there are no proof-labeling schemes involving polynomial-time computation at each node for the whole family of spanning trees with degree at most $OPT+1$. Up to our knowledge, this is the first example of the design of a compact silent self-stabilizing algorithm constructing, and stabilizing on a subset of optimal solutions to a natural problem for which there are no time-efficient proof-labeling schemes. On our way to design our algorithm, we establish a set of independent results that may have interest on their own. In particular, we describe a new space-optimal silent self-stabilizing spanning tree construction, stabilizing on \emph{any} spanning tree, in $O(n)$ rounds, and using just \emph{one} additional bit compared to the size of the labels used to certify trees. We also design a silent loop-free self-stabilizing algorithm for transforming a tree into another tree. Last but not least, we provide a silent self-stabilizing algorithm for computing and certifying the labels of a NCA-labeling scheme

Control Plane in Software Defined Networks and Stateful Data Planes

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