Sébastien Tixeuil

A Distributed TDMA Slot Assignment Algorithm for Wireless Sensor Networks

Wireless sensor networks benefit from communication protocols that reduce power requirements by avoiding frame collision. Time Division Media Access methods schedule transmission in slots to avoid collision, however these methods often lack scalability when implemented in ad hoc networks subject to node failures and dynamic topology. This paper reports a distributed algorithm for TDMA slot assignment that is self-stabilizing to transient faults and dynamic topology change. The expected local convergence time is O(1) for any size network satisfying a constant bound on the size of a node neighborhood.

Self-Stabilizing Systems

This book constitutes the refereed proceedings of the 7th International Symposium on Self-Stabilizing Systems, SSS 2005, held in Barcelona, Spain, in October 2005. The 15 revised full papers presented were carefully reviewed and selected from 33 submissions. The papers address classical topics of self-stabilization, prevailing extensions to the field, such as snap-stabilization, code stabilization, self-stabilization with either dynamic, faulty or Byzantine components, or deal with applications of self-stabilization, either related to operating systems, security, or mobile and ad hoc networks.

Asynchronous mobile robot gathering from symmetric configurations without global multiplicity detection

We consider a set of k autonomous robots that are endowed with visibility sensors (but that are otherwise unable to communicate) and motion actuators. Those robots must collaborate to reach a single vertex that is unknown beforehand, and to remain there hereafter. Previous works on gathering in ringshaped networks suggest that there exists a tradeoff between the size of the set of potential initial configurations, and the power of the sensing capabilities of the robots (i.e. the larger the initial configuration set, the most powerful the sensor needs to be). We prove that there is no such trade off. We propose a gathering protocol for an odd number of robots in a ring-shaped network that allows symmetric but not periodic configurations as initial configurations, yet uses only local weak multiplicity detection. Robots are assumed to be anonymous and oblivious, and the execution model is the non-atomic CORDA model with asynchronous fair scheduling. Our protocol allows the largest set of initial configurations (with respect to impossibility results) yet uses the weakest multiplicity detector to date. The time complexity of our protocol is O(n2), where n denotes the size of the ring. Compared to previous work that also uses local weak multiplicity detection, we do not have the constraint that k < n/2 (here, we simply have 2 < k < n-3).

Self-stabilization in self-organized multihop wireless networks

In large scale multihop wireless networks, flat architectures are not scalable. In order to overcome this major drawback, clusterization is introduced to support self-organization and to enable hierarchical routing. When dealing with multihop wireless networks, the robustness is a main issue due to the dynamicity of such networks. Several algorithms have been designed for the clustering process. As far as we know, very few studies check the robustness feature of their clustering protocols. In this paper, we show that a clustering algorithm, that seems to present good properties of robustness, is self-stabilizing. We propose several enhancements to reduce the stabilization time and to improve stability. The use of a directed acyclic graph ensures that the self-stabilizing properties always hold regardless of the underlying topology. These extra criterion are tested by simulations.

Conflict Managers for Self-stabilization without Fairness Assumption

In this paper, we specify the conflict manager abstraction. Informally, a conflict manager guarantees that any two nodes that are in conflict cannot enter their critical section simultaneously (safety), and that at least one node is able to execute its critical section (progress). The conflict manager problem is strictly weaker than the classical local mutual exclusion problem, where any node that requests to enter its critical section eventually does so (fairness). We argue that conflict managers are a useful mechanism to transform a large class of self-stabilizing algorithms that operate in an essentially sequential model, into self-stabilizing algorithm that operate in a completely asynchronous distributed model. We provide two implementations (one deterministic and one probabilistic) of our abstraction, and provide a composition mechanism to obtain a generic transformer. Our transformers have low overhead: the deterministic transformer requires one memory bit, and guarantees time overhead in order of the network degree, the probabilistic transformer does not require extra memory. While the probabilistic algorithm performs in anonymous networks, it only provides probabilistic stabilization guarantees. In contrast, the deterministic transformer requires initial symmetry breaking but preserves the original algorithm guarantees.

Route preserving stabilization

A distributed system is self-stabilizing if it returns to a legitimate state in a finite number of steps regardless of the initial state, and the system remains in a legitimate state until another fault occurs. A routing algorithm is loop-free if, a path being constructed between two processors p and q, any edges cost change induces a modification of the routing tables in such a way that at any time, there always exists a path from p to q. n nWe present a self-stabilizing loop-free routing algorithm that is also route preserving. This last property means that, a tree being constructed, any message sent to the root is received in a bounded amount of time, even in the presence of continuous edge cost changes. Also, and unlike previous approaches, we do not require that a bound on the network diameter is known to the processors that perform the routing algorithm. We guarantee self-stabilization for many metrics (such as minimum distance, shortest path, best transmitter, depth first search metrics, etc.), by reusing previous results on r-operators.

Optimal Byzantine-resilient convergence in uni-dimensional robot networks

Given a set of robots with arbitrary initial location and no agreement on a global coordinate system, convergence requires that all robots asymptotically approach the exact same, but unknown beforehand, location. Robots are oblivious-they do not recall the past computations-and are allowed to move in a one-dimensional space. Additionally, robots cannot communicate directly, instead they obtain system related information only via visual sensors. Even though convergence and the classical distributed approximate agreement problem (that requires correct processes to decide, for some constant @e, values distance @e apart and within the range of initial proposed values) are similar, we provide evidence that solving convergence in robot networks requires specific assumptions about synchrony and Byzantine resilience. In more detail, we prove necessary and sufficient conditions for the convergence of mobile robots despite a subset of them being Byzantine (i.e. they can exhibit arbitrary behavior). Additionally, we propose two deterministic convergence algorithms for robot networks and analyze their correctness and complexity in various atomicity and synchrony settings. The first algorithm tolerates f Byzantine robots for (2f+1)-sized robot networks in fully synchronous ATOM networks, while the second proposed algorithm tolerates f Byzantine robots for (3f+1)-sized robot networks in non-atomic CORDA networks. The resilience of these two algorithms is proved to be optimal.

Bounding the impact of unbounded attacks in stabilization

As a new challenge of containing the unbounded influence of Byzantine processes in self-stabilizing protocols, this paper introduces a novel concept of strong stabilization. The strong stabilization relaxes the requirement of strict stabilization so that processes beyond the containment radius are allowed to be disturbed by Byzantine processes, but only a limited number of times. A self-stabilizing protocol is (t, c, f)-strongly stabilizing if any process more than c hops away from any Byzantine process is disturbed at most t times in a distributed system with at most f Byzantine processes. Here c denotes the containment radius and t denotes the containment times. n nThe possibility and the effectiveness of the strong stabilization is demonstrated using tree orientation. It is known that the tree orientation has no strictly stabilizing protocol with a constant containment radius. This paper first shows that the problem has no constant bound of the containment radius in a tree with two Byzantine processes even when we allow processes beyond the containment radius to be disturbed any finite number of times. Then we consider the case of a single Byzantine process and present a (1, 0, 1)-strongly stabilizing protocol, which achieves optimality in both containment radius and times.

Optimal deterministic ring exploration with oblivious asynchronous robots

We consider the problem of exploring an anonymous unoriented ring of size n by k identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that k must not divide n for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size n is 4. An upper bound of 17 robots holds in the deterministic case while 4 probabilistic robots are sufficient. In this paper, we close the complexity gap in the deterministic setting, by proving that no deterministic exploration is feasible with less than five robots, and that five robots are sufficient for any n that is coprime with five. Our protocol completes exploration in O(n) robot moves, which is also optimal.

Transient fault detectors

We present fault detectors for transient faults, (i.e., corruptions of the memory of the processors, but not of the code of the processors). We distinguish fault detectors for tasks (i.e., the problem to be solved) from failure detectors for implementations (i.e., the algorithm that solves the problem). The aim of our fault detectors is to detect a memory corruption as soon as possible. We study the amount of memory needed by the fault detectors for some specific tasks, and give bounds for each task. The amount of memory is related to the size and the number of views that a processor has to maintain to ensure a quick detection. This work may give the implementation designer hints concerning the techniques and resources that are required for implementing a task.