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September 2011 - present

September 2000 - August 2011

October 1999 - July 2000

## Publications

Publications (119)

Networks are essential for analyzing complex systems. However, their growing size necessitates backbone extraction techniques aimed at reducing their size while retaining critical features. In practice, selecting, implementing, and evaluating the most suitable backbone extraction method may be challenging. This paper introduces netbone, a Python pa...

The big break in data collection tools of large-scale networks from biological, social, and technological domains expands the challenge of their visualization and processing. Numerous structural and statistical backbone extraction techniques aim to reduce the network’s size while preserving its gist. Here, we perform an experimental comparison of s...

Inspired by the split decomposition of graphs and rank-width, we introduce the notion of $r$-splits. We focus on the family of $r$-splits of a graph of order $n$, and we prove that it forms a hypergraph with several properties. We prove that such hypergraphs can be represented using only $\mathcal O(n^{r+1})$ of its hyperedges, despite its potentia...

Given a non-decreasing sequence $S = (s_{1}, s_{2}, \ldots , s_{k})$ of positive integers, an $S$-packing coloring of a graph $G$ is a partition of the vertex set of $G$ into $k$ subsets $\{V_{1}, V_{2}, \ldots , V_{k}\}$ such that for each $1 \leq i \leq k$, the distance between any two distinct vertices $u$ and $v$ in $V_{i}$ is at least $s_{i} +...

We consider the following list coloring with separation problem: Given a graph $G$ and integers $a,b$, find the largest integer $c$ such that for any list assignment $L$ of $G$ with $|L(v)|= a$ for any vertex $v$ and $|L(u)\cap L(v)|\le c$ for any edge $uv$ of $G$, there exists an assignment $\varphi$ of sets of integers to the vertices of $G$ such...

In this article, we present two deterministic leader election algorithms for programmable matter on the face‐centered cubic grid. The face‐centered cubic grid is a three‐dimensional 12‐regular infinite grid that represents an optimal way to pack spheres (i.e., spherical particles or modules in the context of the programmable matter) in the three‐di...

L’Internet des objets (en anglais Internet of Things, IoT), aujourd’hui omniprésent, a grandement contribué à l’accroissement du trafic des données sur Internet. Les technologies d’accès IoT et les contraintes des objets peuvent causer des problèmes de performances et de sécurité. Cela démontre l’importance des défis liés à cet environnement comme...

L’Internet des objets (en anglais Internet of Things, IoT), aujourd’hui omniprésent, a grandement contribué à l’accroissement du trafic des données sur Internet. Les technologies d’accès IoT et les contraintes des objets peuvent causer des problèmes de performances et de sécurité. Cela démontre l’importance des défis liés à cet environnement comme...

Nowadays, providing Internet of Things (IoT) environments with service level guarantee is a challenging task. Moreover, IoT services should be autonomous in order to minimize human intervention and thus to reduce the operational management cost of the corresponding big scale infrastructure. We describe in this paper a service level-based IoT archit...

Abstract The way nodes are arranged in a wireless network can significantly influence performance, especially information flow. The construction of disjoint virtual backbone networks (DVBNs) is one of the ways this can be accomplished. In this study, the authors first present a proposal that constructs multiple DVBNs using nodes' locations, in two...

In this chapter we introduce the IoT environment through architectures proposed by different standardization bodies. We describe the importance of managing security and the protection of privacy in this kind of environment. Further, the authors highlight the needs and requirements of each layer in the IoT architecture in terms of QoS as well as in...

Telecommunication networks today make it possible to respond to an essential need for all users: the ability to communicate in one's daily and professional life. Wireless networks led to the rise of several categories of services with different characteristics. In recent years, researchers have largely focused on a new category of networks, called...

Energy optimization is essential in IoT environments due to energy constraints for some IoT components. In fact, energy consumption has a direct impact on IoT system lifetime, which represents an important Quality of Service (QoS) parameter for IoT environments. In order to extend the IoT system lifetime, energy consumption optimization should be c...

The study of a variation of the marking game, in which the first player marks vertices and the second player marks edges of an undirected graph was proposed by Bartnicki et al. (Electron J Combin 15:R72, 2008). In this game, the goal of the second player is to mark as many edges around an unmarked vertex as possible, while the first player wants ju...

In this paper, we present two deterministic leader election algorithms for programmable matter on the face-centered cubic grid. The face-centered cubic grid is a 3-dimensional 12-regular infinite grid that represents an optimal way to pack spheres (i.e., spherical particles or modules in the context of the programmable matter) in the 3-dimensional...

Given a graph G and a nondecreasing sequence \(S=(s_1,\ldots ,s_k)\) of positive integers, the mapping \(c:V(G)\longrightarrow \{1,\ldots ,k\}\) is called an S-packing coloring of G if for any two distinct vertices x and y in \(c^{-1}(i)\), the distance between x and y is greater than \(s_i\). The smallest integer k such that there exists a \((1,2,...

Dans ce chapitre de livre, Ahmad Khalil, Nader Mbarek et Olivier Togni présentent l’environnement de type Internet des objets à travers les architectures proposées par différents organismes de standardisation et décrivent l’importance de la gestion de la sécurité et la protection de la vie privée dans ce type d’environnement. De plus, les auteurs m...

Le réseau devient embarqué dans notre vie quotidienne grâce à des composants de plus en plus petits, peu coûteux, puissants, rapides et de plus en plus connectés entre eux. Parallèlement à cette explosion quantitative des réseaux de communication, les technologies se complexifient. Cette évolution s’accompagne de challenges en termes de gestion et...

We consider the following list coloring with separation problem of graphs: Given a graph $G$ and integers $a,b$, find the largest integer $c$ such that for any list assignment $L$ of $G$ with $|L(v)|\le a$ for any vertex $v$ and $|L(u)\cap L(v)|\le c$ for any edge $uv$ of $G$, there exists an assignment $\varphi$ of sets of integers to the vertices...

Access Control is an important security service that should be considered in IoT environments in order to offer reliable IoT services. Access control in IoT environments concerns not only the access of IoT users to IoT services and objects, but also the access of IoT objects to IoT gateways. In this paper, we specify an access control mechanism tha...

In the new technological era called the Internet of Things (IoT), people, machines and objects communicate with each other via the Internet by exchanging information. In this context, trust plays an important role and is considered as a key factor in the success of the IoT services expansion. IoT services and applications use in some cases data con...

Given a graph G, the exact distance-p graph \(G^{[\natural p]}\) has V(G) as its vertex set, and two vertices are adjacent whenever the distance between them in G equals p. We present formulas describing the structure of exact distance-p graphs of the Cartesian, the strong, and the lexicographic product. We prove such formulas for the exact distanc...

Enabling service level guarantee within IoT (Internet of Things) environments is an important and a challenging task in order to enhance user experience while using IoT applications. The corresponding user service level expectations could be specified in a Service Level Agreement (SLA) that we have to conclude with the IoT Service Provider for each...

The context of this paper is programmable matter, which consists of a set of computational elements, called particles, in an infinite graph. The considered infinite graphs are the square, triangular and king grids. Each particle occupies one vertex, can communicate with the adjacent particles, has the same clockwise direction and knows the local po...

Nowadays, providing Internet of Things (IoT) environments with service level guarantee is a challenging task. We describe in this paper a service level based IoT architecture that enables an IoT Service Level Agreement (iSLA) achievement between an IoT Service Provider and an IoT Client. This IoT SLA specifies the requirements of an IoT service in...

The face-centered cubic grid is a three dimensional 12-regular infinite grid. This graph represents an optimal way to pack spheres in the three-dimensional space. We give lower and upper bounds on the chromatic number of the dth power of the face-centered cubic grid. In particular, in the case d = 2 we prove that the chromatic number of this grid i...

A $(a,b)$-coloring of a graph $G$ associates to each vertex a set of $b$ colors from a set of $a$ colors in such a way that the color-sets of adjacent vertices are disjoints. We define general reduction tools for $(a,b)$-coloring of graphs for $2\le a/b\le 3$. In particular, we prove necessary and sufficient conditions for the existence of a $(a,b)...

While wireless sensor networks continue to break new grounds in applications, favored by technological innovations, energy efficiency continues to stagnate. Duty cycling remains the most popular and effective technique used to improve energy efficiency and thus lifetime of the network. Nevertheless, duty cycling imposes temporary unavailability on...

Providing Internet of Things (IoT) environments with service level guarantee is a challenging task for improving IoT application usage experience. We specify in this paper an IoT architecture enabling an IoT Service Level Agreement (iSLA) achievement between an IoT Service Provider (IoT-SP) and an IoT Client (IoT-C). In order to guarantee the IoT a...

Given a graph $G$, the exact distance-$p$ graph $G^{[\natural p]}$ has $V(G)$ as its vertex set, and two vertices are adjacent whenever the distance between them in $G$ equals $p$. We present formulas describing the structure of exact distance-$p$ graphs of the Cartesian, the strong, and the lexicographic product. We prove such formulas for the exa...

Given a graph $G$ and a nondecreasing sequence $S=(s_1,\ldots,s_k)$ of positive integers, the mapping $c:V(G)\longrightarrow \{1,\ldots,k\}$ is called an $S$-packing coloring of $G$ if for any two distinct vertices $x$ and $y$ in $c^{-1}(i)$, the distance between $x$ and $y$ is greater than $s_i$. The smallest integer $k$ such that there exists a $...

The context of this paper is programmable matter, which consists of a set of computational elements, called particles, in an infinite graph. The considered infinite graphs are the square, triangular and king grids. Each particle occupies one vertex, can communicate with the adjacent particles, has the same clockwise direction and knows the local po...

The context of this paper is programmable matter, which consists of a set of computational elements, called particles, in an infinite graph. The considered infinite graphs are the square, triangular and king grids. Each particle occupies one vertex, can communicate with the adjacent particles, has the same clockwise direction and knows the local po...

Providing users with a service level guarantee in the Internet of Things (IoT) is a challenging task in order to ensure a better user experience in such environment. We present in this paper an adaptation of the slotted Carrier-Sense Multiple Access with Collision Avoidance (CSMA/CA) method used in the Media Access Control (MAC layer) of the IEEE 8...

The face-centered cubic grid is a three dimensional 12-regular infinite grid. This graph represents an optimal way to pack spheres in the three-dimensional space. In this grid, the vertices represent the spheres and the edges represent the contact between spheres. We give lower and upper bounds on the chromatic number of the d th power of the face-...

Nowadays, providing Internet of Things (IoT) environments with service level guarantee is a challenging task. We describe in this paper a service level based IoT architecture that enables an IoT Service Level Agreement (iSLA) achievement between an IoT Service Provider and an IoT Client. This IoT SLA specifies the requirements of an IoT service in...

Given a non-decreasing sequence S = (s 1,s 2,. .. ,s k) of positive integers, an S-packing edge-coloring of a graph G is a partition of the edge set of G into k subsets {X 1 ,X 2,. .. ,X k } such that for each 1 $\le$ i $\le$ k, the distance between two distinct edges e, e ' $\in$ X i is at least s i + 1. This paper studies S-packing edge-colorings...

Nowadays, providing IoT environments with service level guarantee is a challenging task. We propose a framework for IoT service level guarantee thanks to several specific Service Level Agreements (SLAs) for IoT environments. We specify different SLAs for each entity contributing in our IoT architecture in order to conclude a global SLA called IoT-S...

The question of whether subcubic graphs have finite packing chromatic number or not is still open although positive responses are known for some subclasses, including subcubic trees, base-3 Sierpiski graphs and hexagonal lattices. In this paper, we answer positively to the question for some subcubic outerplanar graphs. We provide asymptotic bounds...

One serious concern in the ubiquitous networks is the seamless vertical handover management between different wireless technologies. To meet this challenge, many standardization organizations proposed different protocols at different layers of the protocol stack. The Internet Engineering Task Force (IETF) has different groups working on mobility at...

The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by defining (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges,...

Quality of service (QoS) in wireless mesh networks is an active area of research, which is driven by the increasing demand for real-time and multimedia applications, such as Voice over IP and Video on Demand. In this paper, we propose a novel QoS based routing protocol for wireless mesh infrastructure, called Hybrid QoS Mesh Routing (HQMR). It is c...

Gyárfás et al. and Zaker have proven that the Grundy number of a graph $G$ satisfies $\Gamma(G)\ge t$ if and only if $G$ contains an induced subgraph called a $t$-atom.The family of $t$-atoms has bounded order and contains a finite number of graphs.In this article, we introduce equivalents of $t$-atoms for b-coloring and partial Grundy coloring.Thi...

Quality of service (QoS) in wireless mesh networks (WMN) is an active area of research, which is driven by the increasing demand for real-time and multimedia applications, such as VoIP (Voice over IP) and VoD (Video on Demand). In this paper, we propose a QoS multi-tree based routing protocol for wireless mesh en-vironments, named Inter-Mesh Infras...

A graph G is free (a, b)-choosable if for any vertex v with b colors assigned and for any list of colors of size a associated with each vertex (Formula presented.), the coloring can be completed by choosing for u a subset of b colors such that adjacent vertices are colored with disjoint color sets. In this note, a necessary and sufficient condition...

Today, the Cloud networking aspect is a critical factor for adopting the Cloud computing approach. The main drawback of Cloud networking consists in the lack of Quality of Service (QoS) guarantee and management in conformance with a corresponding Service Level Agreement (SLA). This paper presents a framework for resource allocation according to an...

Today, cloud networking which is the ability to connect users with their cloud services and to interconnect these services in an inter-cloud approach, is one of the recent research areas within the cloud computing research communities. The main drawback of cloud networking consists in the lack of Quality of Service (QoS) guarantee and management in...

Wireless Mesh Networks (WMNs) have been considered as a promising alternative to conventional wired networks, thanks to its flexibility and easy deployment. Thus, to ensure a satisfying level of QoS guarantees for real-time and streaming applications such as Voice over IP (VoIP) and Video on Demand (VoD), we propose a novel QoS based routing protoc...

Dans un réseau, la recherche de plusieurs arbres couvrants avec des propriétés intéressantes a amené à l’introduction de plusieurs notions : les arbres couvrants arête-disjoints, les arbres indépendants enracinés en un sommet et les arbres complètement indépendants. Afin de généraliser ces notions, nous introduisons la notion d’arbres couvrants (i,...

Wireless Mesh Networks (WMNs) have been attracting more and more interest from both academic and industrial environments for their seamless broadband connectivity to Internet networks. Besides, providing QoS guarantees for real-time and streaming applications such as Voice over IP (VoIP) and Video on Demand (VoD) is a challenging issue in such envi...

An $i$-packing in a graph $G$ is a set of vertices at pairwise distance
greater than $i$. For a nondecreasing sequence of integers
$S=(s\_{1},s\_{2},\ldots)$, the $S$-packing chromatic number of a graph $G$ is
the least integer $k$ such that there exists a coloring of $G$ into $k$ colors
where each set of vertices colored $i$, $i=1,\ldots, k$, is a...

Gy{\'a}rf{\'a}s et al. and Zaker have proven that the Grundy number of a
graph $G$ satisfies $\Gamma(G)\ge t$ if and only if $G$ contains an induced
subgraph called a $t$-atom. The family of $t$-atoms has bounded order and
contains a finite number of graphs. In this article, we introduce equivalents
of $t$-atoms for b-coloring and partial Grundy co...

Today, cloud networking is one of the recent research areas in the cloud computing research communities. The main drawback of cloud networking consists in the lack of Quality of Service (QoS) guarantee and management in conformance with a corresponding Service Level Agreement (SLA). In this paper, we propose a framework for self-establishing an end...

Let $k\ge 2$ be an integer and $T_1,\ldots, T_k$ be spanning trees of a graph
$G$. If for any pair of vertices $(u,v)$ of $V(G)$, the paths from $u$ to $v$
in each $T_i$, $1\le i\le k$, do not contain common edges and common vertices,
except the vertices $u$ and $v$, then $T_1,\ldots, T_k$ are completely
independent spanning trees in $G$. For $2k$-...

The Grundy number of a graph G, denoted by Gamma(G), is the largest k such that there exists a partition of V(G), into k independent sets V-1, . . . , V-k and every vertex of V-i is adjacent to at least one vertex in V-j, for every j < i. The objects which are studied in this article are families of r-regular graphs such that Gamma(G) = r + 1. Usin...

With the growth of wireless networks, Wireless Mesh Network (WMN) has appeared as an emerging key solution for broadband Internet access with a low-cost deployment. Moreover, providing QoS guarantees for real-time and streaming applications such as VoIP (Voice over IP) and VoD (Video on Demand) is a challenging issue in such environment. In this pa...

Nous étudions l’existence de r arbres couvrants complètement disjoints dans des graphes 2r-réguliers et 2r-connexes, et énonçons des conditions nécessaires à leur existence. Nous déterminons le nombre maximum d’arbres dans les produits cartésiens d’une clique et d’un cycle. Nous montrons que ce nombre n’est pas toujours r.

Today, cloud networking which is the ability to connect the user with his cloud services and to interconnect these services within an inter-cloud approach, is one of the recent research areas in the cloud computing research communities. The main drawback of cloud networking consists in the lack of Quality of Service (QoS) guarantee and management i...

The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest
integer $p$ such that vertices of $G$ can be partitioned into disjoint classes
$X_{1}, ..., X_{p}$ where vertices in $X_{i}$ have pairwise distance greater
than $i$. For $k < t$ we study the packing chromatic number of infinite
distance graphs $D(k, t)$, i.e. graphs with t...

Given a non-decreasing sequence $S=(s_1,s_2, \ldots, s_k)$ of positive integers, an {\em $S$-packing coloring} of a graph $G$ is a mapping $c$ from $V(G)$ to $\{s_1,s_2, \ldots, s_k\}$ such that any two vertices with color $s_i$ are at mutual distance greater than $s_i$, $1\le i\le k$. This paper studies $S$-packing colorings of (sub)cubic graphs....

A key requirement to provide seamless mobility and guaranteeing Quality of Service in heterogeneous environment is to select the best destination network during handover. In this paper, we propose a new schema for network selection based on Multiple Linear Regression Model (MLRM). A horough investigation, on a huge live data collected from GPRS/UMT...

The {\em packing chromatic number} $\chi_{\rho}(G)$ of a graph $G$ is the least integer $k$ for which there exists a mapping $f$ from $V(G)$ to $\{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. This paper studies the packing chromatic number of infinite distance graphs $G(\mathbb{Z},D)$, i.e. graphs with the se...

A graph $G$ is $(a,b)$-choosable if for any color list of size $a$ associated
with each vertex, one can choose a subset of $b$ colors such that adjacent
vertices are colored with disjoint color sets. This paper proves that for any
integer $m\ge 1$, every finite triangle-free induced subgraph of the triangular
lattice is $(5m,2m)$-choosable.

Given a non-decreasing sequence $S=(s_1,s_2, \ldots, s_k)$ of positive
integers, an {\em $S$-packing coloring} of a graph $G$ is a mapping $c$ from
$V(G)$ to $\{s_1,s_2, \ldots, s_k\}$ such that any two vertices with color
$s_i$ are at mutual distance greater than $s_i$, $1\le i\le k$. This paper
studies $S$-packing colorings of (sub)cubic graphs....

A graph $G$ is free $(a,b)$-choosable if for any vertex $v$ with $b$ colors
assigned and for any list of colors of size $a$ associated with each vertex
$u\ne v$, the coloring can be completed by choosing for $u$ a subset of $b$
colors such that adjacent vertices are colored with disjoint color sets. In
this note, a necessary and sufficient conditio...

Today, cloud networking which is the ability to connect the user with his cloud services and to interconnect these services within an inter-cloud approach, is one of the recent research areas in the cloud computing research communities. The main drawback of cloud networking consists in the lack of Quality of Service (QoS) assurance and management i...

Motivated by the Channel Assignment Problem, we study radio k-labelings of graphs. A radio k-labeling of a connected graph G is an assignment c of non-negative integers to the vertices of G such that vertical bar c(x) - c(y)vertical bar >= k + 1 - d(x, y). for any two vertices x and y, x not equal y, where d(x, y) is the distance between x and y in...

Seamless handover between networks in heterogeneous environment is essential to guarantee end-to- end QoS for mobile users. A key requirement is the ability to select seamlessly the next best network. Currently, the implementation of the selection algorithm of the IEEE 802.21 standard by National Institute of Standards and Technology considers only...

Seamless Handover between networks in heterogeneous environment is essential to guarantee end-to-end QoS for mobile users. A key requirement is the ability to select the next best network. Currently, the implementation of the IEEE 802.21 standard by National Institute of Standards and Technology (NIST) considers only the signal strength as a parame...

This paper studies edge- and total-colorings of graphs in which (all or only adjacent) vertices are distinguished by their sets of colors. We provide bounds for the minimum number of colors needed for such colorings for the Cartesian product of graphs along with exact results for generalized hypercubes. We also present general bounds for the direct...