Thibault Bernard

Random walks in distributed computing: a survey

In this survey, we give an overview of the use of random walks as a traversal scheme to derive distributed control algorithms over a network of computers. It is shown that this paradigm for information exchange can be an attractive technique by using electric network theory as a mathematical tool for performance evaluation.

Slot scheduling for wireless sensor networks

In wireless sensor networks WSN, one of the most important challenges is power saving, then various contributions are suggested since a decade. In this paper, we propose a distributed and adaptive gossiping technique able to guarantee communications over all sensors and to save a high amount of energy. The aim is to allow to the network to achieve a self-organizing procedure in order to provide an efficient structuring approach for communications over all sensors. The medium access will be TDMA Time Division Medium Access like. Indeed, each sensor will have a particular slot for listening and another one for sending. The slot assignment is achieved in a distributed manner and is continuously reconfigurable. That means when a sensor leaves the network, its assigned slot will be recovered and when a new one wants to join the network, the last available slot will be assigned to it.

Topological adaptability for the distributed token circulation paradigm in faulty environment

In this paper, we combine random walks and self-stabilization to design a single token circulation algorithm. Random walks have proved their efficiency in dynamic networks and are perfectly adapted to frequent network topological changes. Self-stabilization is the most general technique to design an algorithm that tolerates transient failures. Taking account that the token circulates continually according to a random walk scheme, designing a self-stabilizing algorithm implies to solve two situations (1) no token in the system and (2) several tokens in the system. The former is generally solved by a time-out mechanism, upon timeout a new token is created. In this paper, we focus on this problem. Just state that one may choose a sufficiently long time-out period is not possible in our case: the system could never stabilize. Indeed, a random walk based token eventually cover the network but only the expected time to cover the network can be captured. Therefore, we introduce a mechanism “the reloaded wave propagation” to prevent unnecessary token creation and preserve self-stabilization properties.

Random Distributed Self-stabilizing Structures Maintenance

Self-stabilization is a solution for many fault-tolerance problems. In this paper, we present a self-stabilizing solution to compute random local spanning trees rooted in each site. The computation is achieved thanks to random walks. We present an algorithm that works in a fully distributed environment: asynchronous message passing model is used.

A low energy consumption MAC protocol for WSN

The design of an energy-efficient Medium Access Control (MAC) protocol is one of the major issues in wireless sensor networks (WSN). In this study, we present a MAC protocol adapted to a particular class of WSNs. This protocol is mainly used for nodes located in the same radio range. It could be used by WSNs dedicated to environment monitoring where each node senses a parameter periodically. In this particular case, a node executes a code during a small period and in the rest of the time it moves to a sleeping mode. Our protocol maintains a abstract ring which ensures the ordered communications and avoids collisions. The actual version of the technique is one-hop based communication. The multi-hop extension is discussed in the paper.

A new method to automatically compute processing times for random walks based distributed algorithms

Random walks constitute an attractive technique in distributed computing. In this paper, we present an original method using relationship between electrical resistance and random walks, to automatically compute quantities such as cover time, and more generally any processing time measure defined through hitting times. This method comes from electrical theory by using Millmans theorem.

A distributed clustering algorithm for large-scale dynamic networks

We propose an algorithm that builds and maintains clusters over a network subject to mobility. This algorithm is fully decentralized and makes all the different clusters grow concurrently. The algorithm uses circulating tokens that collect data and move according to a random walk traversal scheme. Their task consists in (i) creating a cluster with the nodes it discovers and (ii) managing the cluster expansion; all decisions affecting the cluster are taken only by a node that owns the token. The size of each cluster is maintained higher than m nodes (m is a parameter of the algorithm). The obtained clustering is locally optimal in the sense that, with only a local view of each clusters, it computes the largest possible number of clusters (i.e. the sizes of the clusters are as close to m as possible). This algorithm is designed as a decentralized control algorithm for large scale networks and is mobility-adaptive: after a series of topological changes, the algorithm converges to a clustering. This recomputation only affects nodes in clusters where topological changes happened, and in adjacent clusters.

Efficient Communications over Wireless Sensor Networks

Power saving is a very critical issue in energyconstrained wireless sensor networks. Many schemes can be found in the literature, which have significant contributions in energy conservation. The aim of this study is to propose a distributed technique able to guarantee communications over all sensors and reducing in a considerable rate the energy consumed. The originality of the solution is the use fundamental principles inherited from distributed computing (leader election, consensus, abstract ring structure). The aim is to allow to the network to achieve a self organizing procedure which assigns a slot time to each sensor. Indeed, each sensor will have a particular slot for listening and another one for sending. The slot assignment is done in distributed manner and can adapted dynamically.

Decentralized resources management for grid

Among all components of a grid or peer-to-peer application, the resources management is unavoidable Indeed, new resources like computational power or storage capacity must be quickly and efficiently integrated This management can be achieved either by a fully centralized way (BOINC) or by a hierarchical way (Globus, DIET) In the latter case, there is a greater flexibility and a greater scalability But the counterpart is the difficulty to design and to deploy such a solution, particularly if the resources are volatile. In this article, we combine random walks and circulating word to derive a fully distributed solution to the resources management Random walks have proved their efficiency in distributed computing and are well suited to dynamical networks like peer-to-peer or grid networks There is no condition on nodes lifetime and we need only one application for each node.

Universal adaptive self-stabilizing traversal scheme: Random walk and reloading wave

In this paper, we investigate random walk based token circulation in dynamic environments subject to faults. We describe hypotheses on the dynamic environment that allow random walks to meet the important property that the token visits any node infinitely often. The randomness of this scheme allows it to work on any topology, and requires no adaptation after a topological change, which is a desirable property for applications to dynamic systems. For random walks to be a traversal scheme and to solve the concurrency problem, one needs to guarantee that exactly one token circulates in the system. In the presence of transient faults, configurations with multiple tokens or with no token can occur. The meeting property of random walks solves the cases with multiple tokens. The reloading wave mechanism we propose, together with timeouts, allows us to detect and solve cases with no token. This traversal scheme is self-stabilizing, and universal, meaning that it needs no assumption on the system topology. We describe conditions on the dynamicity (with a local detection criterion) under which the algorithm is tolerant to dynamic reconfigurations. We conclude with a study on the time between two visits of the token to a node, which we use to tune the parameters of the reloading wave mechanism according to some system characteristics.