Section: New Results

Algorithms and estimation for graph data

Modelisation of networks of multiagent systems

Participants: Aurélie Muller-Gueudin

We relate here a collaboration with researchers in Automatic in Nancy (CRAN).

We consider here networks, modeled as a graph with nodes and edges representing the agents and their interconnections, respectively. The connectivity of the network, persistence of links and interactions reciprocity influence the convergence speed towards a consensus.

The problem of consensus or synchronization is motivated by different applications as communication networks, power and transport grids, decentralized computing networks, and social or biological networks.

We then consider networks of interconnected dynamical systems, called agents, that are partitioned into several clusters. Most of the agents can only update their state in a continuous way using only inner-cluster agent states. On top of this, few agents also have the peculiarity to rarely update their states in a discrete way by reseting it using states from agents outside their clusters. In social networks, the opinion of each individual evolves by taking into account the opinions of the members belonging to its community. Nevertheless, one or several individuals can change its opinion by interacting with individuals outside its community. These inter-cluster interactions can be seen as resets of the opinions. This leads us to a network dynamics that is expressed in term of reset systems. We suppose that the reset instants arrive stochastically following a Poisson renewal process.

We have an accepted paper in the journal IEEE Transactions on Automatic Control [6].

Compression and analysis of trees

Participant: Romain Azaïs

External participants: Jean-Baptiste Durand (ENSIMAG, Inria MISTIS), Christophe Godin (Inria Virtual Plants), Benoît Henry (Inria TOSCA puis Madynes), Alexandre Genadot (Université de Bordeaux, Inria CQFD)

Tree-structured data naturally appear in various fields, particularly in biology where plants and blood vessels may be described by trees, but also in computer science because XML documents form a tree structure. Among trees, the class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In a recent preprint [28], we provide a better combinatorial characterization of this specific family of trees. We show that self-nested trees may be considered as a good approximation class of unordered trees. In addition, we compare our approximation algorithms with a competitive approach of the literature on a simulated dataset. On the other hand, the paper [30] is devoted to the estimation of the relative scale of ordered trees that share the same layout. The theoretical study is achieved for the stochastic model of conditioned Galton-Watson trees. New estimators are introduced and their consistency is stated. A comparison is made with an existing approach of the literature. A simulation study shows the good behavior of our procedure on finite-sample sizes. An application to the analysis of revisions of Wikipedia articles is also considered through real data.