Devan Sohier

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.

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.

Space-Optimal Counting in Population Protocols

In this paper, we study the fundamental problem of counting, which consists in computing the size of a system. We consider the distributed communication model of population protocols of finite state, anonymous and asynchronous mobile devices agents communicating in pairs according to a fairness condition. This work significantly improves the previous results known for counting in this model, in terms of exact space complexity. We present and prove correct the first space-optimal protocols solving the problem for two classical types of fairness, global and weak. Both protocols require no initialization of the counted agents. The protocol designed for global fairness, surprisingly, uses only one bit of memory two states per counted agent. The protocol, functioning under weak fairness, requires the necessary

Improving SEU fault tolerance capabilities of a self-converging algorithm

\log P

Self-stabilizing hierarchical construction of bounded size clusters

bits P states, per counted agent to be able to count up to P agents. Interestingly, this protocol exploits the intriguing Gros sequence of natural numbers, which is also used in the solutions to the Chinese Rings and the Hanoi Towers puzzles.

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

Self-convergence is a property of distributed systems, allowing a system, when it was perturbed or badly initialised, to recover a correct operation in a finite number of calculation steps. In this paper is explored the intrinsic robustness of a self converging algorithm with respect to soft errors resulting from SEU (Single Event Upset) phenomena. This study was performed by fault injection using a devoted test platform. A self-converging benchmark program was executed by a LEON3 processor implemented in an FPGA. The low number of observed errors puts in evidence the fault tolerance of the tested algorithm.

Distributed Construction of Nested Clusters with Inter-cluster Routing

The single-event upset (SEU) fault tolerance of a benchmark self-converging algorithm is evaluated by fault injection campaigns performed using a devoted test platform. The number of observed errors significantly decreases depending on adopted implementation strategies.