Swan Dubois

Bounding the Impact of Unbounded Attacks in Stabilization

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permit to cope with arbitrary malicious behaviors. Combining these two properties proved difficult: it is impossible to contain the spatial impact of Byzantine nodes in a self-stabilizing context for global tasks such as tree orientation and tree construction. We present and illustrate a new concept of Byzantine containment in stabilization. Our property, called Strong Stabilization enables to contain the impact of Byzantine nodes if they actually perform too many Byzantine actions. We derive impossibility results for strong stabilization and present strongly stabilizing protocols for tree orientation and tree construction that are optimal with respect to the number of Byzantine nodes that can be tolerated in a self-stabilizing context.

On byzantine containment properties of the min + 1 protocol

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. We consider the well known problem of constructing a breadth-first spanning tree in this context. Combining these two properties prove difficult: we demonstrate that it is impossible to contain the impact of Byzantine processes in a strictly or strongly stabilizing manner. We then adopt the weaker scheme of topology-aware strict stabilization and we present a similar weakening of strong stabilization. We prove that the classical min+1 protocol has optimal Byzantine containment properties with respect to these criteria.

The impact of topology on Byzantine containment in stabilization

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. We consider the well known problem of constructing a maximum metric tree in this context. Combining these two properties proves difficult: we demonstrate that it is impossible to contain the impact of Byzantine nodes in a self-stabilizing context for maximum metric tree construction (strict stabilization). We propose a weaker containment scheme called topology-aware strict stabilization, and present a protocol for computing maximum metric trees that is optimal for this scheme with respect to impossibility result.

Maximum Metric Spanning Tree Made Byzantine Tolerant

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. This paper focuses on systems that are both self-stabilizing and Byzantine tolerant. Combining these two properties is known to induce many impossibility results. Hence, there exist several fault tolerance schemes to contain Byzantine faults in self-stabilization. In this paper, we consider the well known problem of constructing a maximum metric tree in this context. We provide a new distributed protocol that ensures the best possible containment with respect to topology-aware strict and strong stabilization.

Maximum metric spanning tree made Byzantine tolerant

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. This paper focuses on systems that are both self-stabilizing and Byzantine tolerant. We consider the well known problem of constructing a maximum metric tree in this context. Combining these two properties is known to induce many impossibility results. In this paper, we first provide two new impossibility results about the construction of a maximum metric tree in presence of transient and (permanent) Byzantine faults. Then, we propose a new self-stabilizing protocol that provides optimal containment to an arbitrary number of Byzantine faults.

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 an optimal stabilizing data-link layer that emulates a reliable FIFO communication channel over unreliable capacity bounded non-FIFO channels (the channel capacity is known to the protocol).

Practically stabilizing SWMR atomic memory in message-passing systems

A fault-tolerant and practically stabilizing simulation of an atomic register is presented. The simulation works in asynchronous message-passing systems, and allows a minority of processes to crash. The simulation stabilizes in a practically stabilizing manner, by reaching a long execution in which it runs correctly. A key element in the simulation is a new combinatorial construction of a bounded labeling scheme accommodating arbitrary labels, including those not generated by the scheme itself.

A snap-stabilizing point-to-point communication protocol 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 informations given by a routing algorithm. By the context of stabilization (in particular, the system starts in any configuration), these informations 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 informations are initially corrupted.

Pragmatic self-stabilization of atomic memory in message-passing systems

A fault-tolerant and stabilizing simulation of an atomic register is presented. The simulation works in asynchronous message-passing systems, and allows a minority of processes to crash. The simulation stabilizes in a pragmatic manner, by reaching a long execution in which it runs correctly. A key element in the simulation is a new combinatorial construction of a bounded labeling scheme accommodating arbitrary labels, including those not generated by the scheme itself.

Enabling Minimal Dominating Set in Highly Dynamic Distributed Systems

We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make only weak assumptions on the communication: every process is infinitely often able to communicate with other processes not necessarily directly. Our contribution is threefold. First, we propose a new definition of minimal dominating set suitable for the context of time-varying graphs that seems more relevant than existing ones. Next, we provide a necessary and sufficient topological condition for the existence of a deterministic algorithm for minimal dominating set construction in our settings. Finally, we propose a new measure of time complexity in time-varying graph in order to allow fair comparison between algorithms. Indeed, this measure takes account of communication delays attributable to dynamicity of the graph and not to the algorithms.