Benoît Henry’s research while affiliated with IMT Nord Europe and other places

We investigate some aspects of the problem of the estimation of birth distributions (BDs) in multi-type Galton–Watson trees (MGWs) with unobserved types. More precisely, we consider two-type MGWs called spinal-structured trees. This kind of tree is characterized by a spine of special individuals whose BD $\nu$ is different from the other individuals in the tree (called normal, and whose BD is denoted by $\mu$ ). In this work, we show that even in such a very structured two-type population, our ability to distinguish the two types and estimate $\mu$ and $\nu$ is constrained by a trade-off between the growth-rate of the population and the similarity of $\mu$ and $\nu$ . Indeed, if the growth-rate is too large, large deviation events are likely to be observed in the sampling of the normal individuals, preventing us from distinguishing them from special ones. Roughly speaking, our approach succeeds if $r\lt \mathfrak{D}(\mu,\nu)$ , where r is the exponential growth-rate of the population and $\mathfrak{D}$ is a divergence measuring the dissimilarity between $\mu$ and $\nu$ .

We investigate some aspects of the problem of the estimation of birth distributions (BD) in multi-type Galton-Watson (MGW) trees with unobserved types. More precisely, we consider a two-type MGW called spinal-structured trees. This kind of tree is characterized by a spine of special individuals whose BD $\nu$ is different from the other individuals in the tree (called normal whose BD is denoted $\mu$). In this work, we show that even in such a very structured two-types population, our ability to distinguish the two types and estimate $\mu$ and $\nu$ is constrained by a trade off between the growth-rate of the population and the similarity of $\mu$ and $\nu$. Indeed, if the growth-rate is too large, large deviations events are likely to be observed in the sampling of the normal individuals preventing us to distinguish them from special ones. Roughly speaking, our approach succeed if $r<\mathfrak{D}(\mu,\nu)$ where r is the exponential growth-rate of the population and $\mathfrak{D}$ is a divergence measuring the dissimilarity between $\mu$ and $\nu$.

Existing shortest path-based routing in wide area networks or equal cost multi-path routing in data center networks do not consider the load on the links while taking routing decisions. As a consequence, an influx of network traffic stemming from events such as distributed link flooding attacks and data shuffle during large scale analytics can congest network links despite the network having sufficient capacity on alternate paths to absorb the traffic. This can have several negative consequences such as service unavailability, delayed flow completion, packet losses, among others. In this regard, we propose SPONGE, a traffic engineering mechanism for handling sudden influx of network traffic. SPONGE models the network as a stochastic process, takes the switch queue occupancy and traffic rate as inputs, and leverages the multiple available paths in the network to route traffic in a way that minimizes the overall packet loss in the network. We demonstrate the practicality of SPONGE through an OpenFlow based implementation, where we periodically and pro-actively reroute network traffic to the routes computed by SPONGE. Mininet emulations using real network topologies show that SPONGE is capable of reducing packet drops by 20% on average even when the network is highly loaded because of an ongoing link flooding attack.

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. This paper 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.

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. This paper is devoted to the estimation of the relative scale parameter 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 and from missing or noisy data. An application to the analysis of revisions of Wikipedia articles is also considered through real data.