Section: New Results
Distributed algorithms
Participants : Luciana Arantes [ correspondent ] , Maria Gradinariu [ correspondent ] , Mathieu Bouillaguet, Pierre Sens, Julien Sopena.
Our current research in the context of distributed algorithms focuses on two main axes. We are interested in providing faulttolerant and self*(selforganizing, selfhealing and selfstabilizing) solutions for fundamental problems in distributed computing. More precisely, we target the following basic blocks: mutual exclusion, resources allocation, agreement and communication primitives. We propose solutions for both static (eg. grid) and dynamic networks (P2P and mobile networks).
Static systems
In 2009, we have proposed a fault tolerant permissionbased kmutual exclusion which does not rely on timers, nor does on failure detectors, neither needs extra messages for detecting node failures. Fault tolerance is integrated in the algorithm itself and it is provided if the underlying system guarantees a Responsiveness Property. Based on Raymond's algorithm, our algorithm exploits the requestreply messages exchanged by processes to get access to one of the k units of the shared resource in order to dynamically detect failures and adapt the algorithm to tolerate them. This work was published in [27] .
Recently we started to investigate two communication abstractions in asynchronous systems under various class of faults. The first abstraction deals with synchronizing logical clocks of neighboring nodes also known as unisson. We study the FTSS (fault tolerant and selfstabilizing) version of the problem in asynchronous settings. We addressed both the crash and Byzantine faults in [39] . The major contribution of our work steams in exploring for the first time the limits of FTSS unisson in asynchronous setting exploring both the impossibility and possibility results.
The second abstraction addresses the FTSS coloring of undirected networks. Coloring has a direct application in the implementation of TDMA communication which is one of the most efficient collision free communication primitives for adhoc networks. In [23] we propose some impossibility results and a deterministic solution that work under restricted schedulers. We extend the study in [22] by proposing probabilistic solutions for asynchronous networks.
Dynamic systems
In this context we are interested in designing building blocks for distributed applications such as: failure detectors, adequate communication primitives (publish/subscribe) and overlays. Moreover, we are interested in solving fundamental problems such as leader election, membership and naming.

In 2009, we start exploiting the dynamics of MANETs in order to propose a distributed computing model that characterize as much as possible the dynamic and selforganizing behavior of MANETs'. The temporal variations in the network topology implies that MANET can not be viewed as a static connected graph over which paths between nodes are established beforehand. Path between two nodes is in fact built over the time. Furthermore, lack of connectivity between nodes (temporal or not) makes of MANET a partitionable system , i.e., a system in which nodes that do not crash or leave the system might be not capable to communicate between themselves. To this end, a first work is published in [20] and a second work has been submitted to publication [58] .

One of the main challenges of DelayTolerant Networks (DTNs) is on how to define effective routing protocols. Both the dynamics of DTNs and network disruptions make the choice of a routing protocol and its performance evaluation non trivial tasks. Hence, our proposal was to use a graph theoretic model, in particular the Evolving Graph (EG) theory, in order to provide a framework for evaluating least cost routing algorithms which exploit different metrics. Concisely, an EG is a timestep indexed sequence of subgraphs, where the subgraph at a given timestep corresponds to the network connectivity at the time interval indicated by the timestep value. The results of the above mentioned evaluation has been published in [19] .

The main challenges of our research activity over 2009 year were to develop self* (selfstabilizing, selforganizing and selfhealing) local algorithms for dynamic networks (P2P, sensor and robot networks). We addressed fundamental problems such as constructions of fault tolerant and reliable infrastructures for networks hit by topological dynamicity. In [24] we study the construction of selfstabilizing Steiner trees in dynamic netwprks. In [25] we address the one to optimal selfstabilizing construction of minimum spanning trees while in [26] we extend the study to the loopfree solutions. That is, solutions where during the dynamicity periods the existing tree is always maintained. Furthermore we investigated faulttolerant agreement in robot networks under various forms of constraints([29] , [28] , [30] ).

Another ongoing research work focuses on trust assessment in dynamic systems. Even if it is near impossible to fully trust a node in a P2P system, managing a set of the most trusted nodes in the system can help to implement more trusted and reliable services. Using these nodes can reduce the probability of introducing malicious nodes in distributed computations. Our work aims at the following objectives: 1. To design a distributed membership algorithm for structured Peer to Peer networks in order to build a group of trusted nodes. 2. To design a maintenance algorithm to periodically clean the trusted group so as to avoid nodes whose reputation has decreased under the minimum value. 3. To provide a way for a given node X to find at least one trusted node. 4. To design a prototype of an information system, such as a news dissemination system, that relies on the trusted group.