Vlady Ravelomanana

Efficient Location Training Protocols for Heterogeneous Sensor and Actor Networks

In this work, we consider a large-scale geographic area populated by tiny sensors and some more powerful devices called actors, authorized to organize the sensors in their vicinity into short-lived, actor-centric sensor networks. The tiny sensors run on miniature nonrechargeable batteries, are anonymous, and are unaware of their location. The sensors differ in their ability to dynamically alter their sleep times. Indeed, the periodic sensors have sleep periods of predefined lengths, established at fabrication time; by contrast, the free sensors can dynamically alter their sleep periods, under program control. The main contribution of this work is to propose an energy-efficient location training protocol for heterogeneous actor-centric sensor networks where the sensors acquire coarse-grain location awareness with respect to the actor in their vicinity. Our theoretical analysis, confirmed by experimental evaluation, shows that the proposed protocol outperforms the best previously known location training protocols in terms of the number of sleep/awake transitions, overall sensor awake time, and energy consumption.

Distributed k-clustering algorithms for random wireless multihop networks

Ad hoc networks consist of wireless hosts that communicate without the need of any fixed infrastructure. A k-clustering protocol is an algorithm in which the wireless network is divided into non-overlapping sub networks, referred to as clusters, and where every node of a sub network is at most k hops from a distinguished station called the clusterhead. Clustering is commonly used in ad hoc networks in order to limit the amount of routing information stored and maintained at individual nodes. In our setting, a large number n of distinguishable stations (e.g. sensors) are randomly deployed in a given area of size |

Cooperative training for high density sensor and actor networks

{\mathcal S}

Creation and growth of components in a random hypergraph process

| We assume that the nodes use synchronous radio transmissions and any pair of nodes u and v are able to communicate if they are within a distance less than their transmitting range of each other. Moreover, if more than two neighbors of a node u transmit simultaneously, u is assumed to receive no message (collision). Under these assumptions, we propose and analyze efficient and fully distributed algorithms for the k-clustering problem.

Quasi-optimal energy-efficient leader election algorithms in radio networks

Exploiting high density features of wireless sensor networks represents a challenging issue. In this context, anonymous, asynchronous and randomly distributed sensors are considered along with few devices, called actors, which are more powerful than sensors in terms of energy and transmission capabilities. The paper proposes a new distributed training protocol for coarse-grain localization purposes in high density environments. The aim is to auto-organize the sensors with respect to a virtual infrastructure centered at actors and constituted of concentric rings divided into sectors. Analytical study as well as experiments on the proposed protocol are provided. The obtained results show under which theoretical and practical settings the training process can be performed in a fast and high quality way with respect to the granularity of the required localization and the energy consumption.

The Average Size of Giant Components between the Double-Jump

Denote by an l-component a connected b-uniform hypergraph with k edges and k(b–1) – l vertices. We prove that the expected number of creations of l-component during a random hypergraph process tends to 1 as l and b tend to ∞ with the total number of vertices n such that

Cooperative Training in Wireless Sensor and Actor Networks

\ell = o\left( \sqrt[3]{\frac{n}{b}} \right)

Efficient binary schemes for training heterogeneous sensor and actor networks

. Under the same conditions, we also show that the expected number of vertices that ever belong to an l-component is approximately 121/3 (b–1)1/3 l1/3n2/3. As an immediate consequence, it follows that with high probability the largest l-component during the process is of size O( (b–1)1/3 l1/3n2/3 ). Our results give insight about the size of giant components inside the phase transition of random hypergraphs.

Another proof of Wright's inequalities

Radio networks (RN) are distributed systems (ad hoc networks) consisting in n>=2 radio stations. Assuming the number n unknown, two distinct models of RN without collision detection (no-CD) are addressed: the model with weak no-CD RN and the one with strong no-CD RN. We design and analyze two distributed leader election protocols, each one running in each of the above two (no-CD RN) models, respectively. Both randomized protocols are shown to elect a leader within O(log(n)) expected time, with no station being awake for more than O(loglog(n)) time slots (such algorithms are said to be energy-efficient). Therefore, a new class of efficient algorithms is set up that match the @W(log(n)) time lower-bound established by Kushilevitz and Mansour [E. Kushilevitz, Y. Mansour, An @W(Dlog(N/D)) lower-bound for broadcast in radio networks, SIAM J. Comp. 27 (1998) 702-712).].

Forbidden subgraphs in connected graphs

AbstractWe study the sizes of connected components according to their excesses during a random graph process built with n vertices. The considered model is the continuous one defined in [17]. An ℓ-component is a connected component with ℓ edges more than vertices. ℓ is also called the excess of such a component. As our main result, we show that when ℓ and n/ℓ are both large, the expected number of vertices that ever belong to an ℓ-component is about 121/3 ℓ1/3 n2/3. We also obtain limit theorems for the number of creations of ℓ-components.