# Stéphane Pérennes's research while affiliated with Université Côte d'Azur and other places

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## Publications (191)

The degree distributions of complex networks are usually considered to follow a power law distribution. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-wor...

We study opinion dynamics in multi-agent networks where agents hold binary opinions and are influenced by their neighbors while being biased towards one of the two opinions, called the superior opinion. The dynamics is modeled by the following process: at each round, a randomly selected agent chooses the superior opinion with some probability α, an...

The clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be of great interest to describe the characteristics of a social graph. But, the clustering coefficient is originally defined for a graph in which the links are undirect...

In the eternal domination game played on graphs, an attacker attacks a vertex at each turn and a team of guards must move a guard to the attacked vertex to defend it. The guards may only move to adjacent vertices on their turn. The goal is to determine the eternal domination number \(\gamma ^{\infty }_{all}\) of a graph, which is the minimum number...

More than ever, data networks have demonstrated their central role in the world economy, but also in the well-being of humanity that needs fast and reliable networks. In parallel, with the emergence of Network Function Virtualization (NFV) and Software Defined Networking (SDN), efficient network algorithms considered too hard to be put in practice...

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-world network. The mai...

We study here the clustering of directed social graphs. The clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be of great interest to describe the characteristics of a social graph. In fact, the clustering coefficient is ad...

In the localization game, introduced by Seager in 2013, an invisible and immobile target is hidden at some vertex of a graph G. At every step, one vertex v of G can be probed which results in the knowledge of the distance between v and the secret location of the target. The objective of the game is to minimize the number of steps needed to locate t...

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-world network. The mai...

We study here the clustering of directed social graphs. The clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be of great interest to describe the characteristics of a social graph. In fact, the clustering coefficient is ad...

In the Spy game played on a graph G, a single spy travels the vertices of G at speed s, while multiple slow guards strive to have, at all times, one of them within distance d of that spy. In order to determine the smallest number of guards necessary for this task, we analyze the game through a Linear Programming formulation and the fractional strat...

In the eternal domination game played on graphs, an attacker attacks a vertex at each turn and a team of guards must move a guard to the attacked vertex to defend it. The guards may only move to adjacent vertices on their turn. The goal is to determine the eternal domination number of a graph which is the minimum number of guards required to defend...

Seager introduced the following game in 2013. An invisible and immobile target is hidden at some vertex of a graph G. Every step, one vertex v of G can be probed which results in the knowledge of the distance between v and the target. The objective of the game is to minimize the number of steps needed to locate the target, wherever it is. We addres...

We define and study the following two-player game on a graph G. Let k∈N⁎. A set of k guards is occupying some vertices of G while one spy is standing at some node. At each turn, first the spy may move along at most s edges, where s∈N⁎ is his speed. Then, each guard may move along one edge. The spy and the guards may occupy the same vertices. The sp...

In this paper, we propose and analyze a simple local algorithm to balance a tree. The motivation comes from live distributed streaming systems in which a source diffuses a content to peers via a tree, a node forwarding the data to its children. Such systems are subject to a high churn, peers frequently joining and leaving the system. It is thus cru...

Motivated by an assignment problem arising in MapReduce computations, we investigate a generalization of the Bin Packing problem which we call Bin Packing with Colocations Problem. We are given a weigthed graph \(G=(V,E)\), where V represents the set of items with positive integer weights and E the set of related (to be colocated) items, and an int...

The (edge) forwarding index of a graph is the minimum, over all possible routings of all the demands, of the maximum load of an edge. This metric is of a great interest since it captures the notion of global congestion in a precise way: the lesser the forwarding-index, the lesser the congestion. In this paper, we study the following design question...

A routing R of a connected graph G is a collection that contains simple paths connecting every ordered pair of vertices in G. The edge-forwarding index with respect to R (or simply the forwarding index with respect to R) π(G,R) of G is the maximum number of paths in R passing through any edge of G. The forwarding index π(G) of G is the minimum π(G,...

The (edge) forwarding index of a graph is the minimum, over all possible rout-ings of all the demands, of the maximum load of an edge. This metric is of a great interest since it captures the notion of global congestion in a precise way: the lesser the forwarding-index, the lesser the congestion. In this paper, we study the following design questio...

The (edge) forwarding index of a graph is the minimum, over all possible routings of all the demands, of the maximum load of an edge. This metric is of a great interest since it captures the notion of global congestion in a precise way: the lesser the forwarding-index, the lesser the congestion. In this paper, we study the following design question...

In telecommunication networks, packets are carried from a source to a destination on a path determined by the underlying routing protocol. Most routing protocols belong to the class of shortest path routing protocols. In such protocols, the network operator assigns a length to each link. A packet going from to follows a shortest path according to t...

In a P2P storage system using erasure codes, a data block is encoded in many redundancy fragments. These fragments are then sent to distinct peers of the network. In this work, we study the impact of different placement policies of these fragments on the performance of storage systems. Several practical factors (easier control, software reuse, late...

A routing R of a connected graph G is a collection that contains simple paths connecting every ordered pair of vertices in G. The edge-forwarding index with respect to R (or simply the forwarding index with respect to R) π(G, R) of G is the maximum number of paths in R passing through any edge of G. The forwarding index π(G) of G is the minimum π(G...

The surveillance game [Fomin et al., 2012] models the problem of web-page prefetching as a pursuit evasion game played on a graph. This two-player game is played turn-by-turn. The first player, called the observer, can mark a fixed amount of vertices at each turn. The second one controls a surfer that stands at vertices of the graph and can slide a...

The notion of Shared Risk Link Groups (SRLG) captures survivability issues when a set of links of a network may fail simultaneously. The theory of survivable network design relies on basic combinatorial objects that are rather easy to compute in the classical graph models: shortest paths, minimum cuts, or pairs of disjoint paths. In the SRLG contex...

A proper coloring of a graph is a partition of its vertex set into stable sets, where each part corresponds to a {\it color}. For a vertex-weighted graph, the {\it weight of a color} is the maximum weight of its vertices. The {\it weight of a coloring} is the sum of the weights of its colors. Guan and Zhu defined the {\it weighted chromatic number}...

An (n,k,r)(n,k,r)-network is a triple N=(G,in,out)N=(G,in,out) where G=(V,E)G=(V,E) is a graph and in,outin,out are non-negative integer functions defined on V called the input and output functions, such that for any v∈Vv∈V, in(v)+out(v)+deg(v)≤2rin(v)+out(v)+deg(v)≤2r where deg(v)deg(v) is the degree of v in the graph G . The total number of input...

In Graph Searching, a team of searchers aims at capturing an invisible fugitive moving arbitrarily fast in a graph. Equivalently, the searchers try to clear a contaminated network.The problem is to compute the minimum number of searchers required to accomplish this task. Several variants of Graph Searching have been studied mainly because of their...

During the last decades, many combinatorial games involving two persons playing on a (directed) graph have received a lot of attention. Some examples of such games are the Angel problem, the Cops and Robbers, the Surveillance game, the Eternal Dominating Set and Eternal Set Cover. One of the main questions in these games is to decide if a given pla...

Let P be a family of dipaths of a DAG (Directed Acyclic Graph) G. The load of an arc is the number of dipaths containing this arc. Let π(G, P) be the maximum of the load of all the arcs and let w(G, P) be the minimum number of wavelengths (colors) needed to color the family of dipaths P in such a way that two dipaths with the same wavelength are ar...

In this paper, we analyze a highly distributed backup storage system realized by means of nano datacenters (NaDa). NaDa have been recently proposed as a way to mitigate the growing energy, bandwidth and device costs of traditional data centers, following the popularity of cloud computing. These service provider-controlled peer-to-peer systems take...

We consider the following Minimum Connectivity Inference problem (MCI), which arises in structural biology: given vertex sets V i ⊆ V, i ∈ I, find a graph G = (V,E) minimizing the size of the edge set E, such that the sub-graph of G induced by each V i is connected. This problem arises in structural biology, when one aims at finding the pairwise co...

In telecommunication networks packets are carried from a source s to a destination t on a path that is determined by the underlying routing protocol. Most routing protocols belong to the class of shortest path routing protocols. In such protocols, the network operator assigns a length to each link. A packet going from s to t follows a shortest path...

In this paper, we propose and study analytical models of self-repairing peer-to-peer storage systems subject to failures. The failures correspond to the simultaneous loss of multiple data blocks due to the definitive loss of a peer (or following a disk crash). In the system we consider that such failures happen continuously, hence the necessity of...

In this paper, we propose and analyze a simple localized algorithm to balance a tree. The motivation comes from live distributed streaming systems in which a source diffuses a content to peers via a tree, a node forwarding the data to its children. Such systems are subject to a high churn, peers frequently joining and leaving the system. It is thus...

The Autonomous System (AS)-level topology of the Internet that currently comprises 40k ASs, is growing at a rate of about 10% per year. In these conditions, Border Gateway Protocol (BGP), the inter-domain routing protocol of the Internet starts to show its limits, among others in terms of the number of routing table entries it can dynamically proce...

Les réseaux de communications sont devenus très complexes de nos jours. Cependant, depuis leur tout début avec ARPANET, les chercheurs et les ingénieurs ont conçu plusieurs protocoles aux divers équipements de ces réseaux afin de réduire cette complexité et d'atteindre la meilleure performance possible du réseau. OSPF ("Open Shortest Path First") e...

The Autonomous System (AS) topology of the Internet (up to 61k ASs) is
growing at a rate of about 10% per year. The Border Gateway Protocol (BGP)
starts to show its limits in terms of the number of routing table entries it
can dynamically process and control. Due to the increasing routing information
processing and storage, the same trend is observ...

In this article we provide hardness results and approximation algorithms for the following three natural degree-constrained subgraph problems, which take as input an undirected graph G=(V,E). Let d>=2 be a fixed integer. The Maximumd-degree-bounded Connected Subgraph (MDBCS"d) problem takes as additional input a weight function @w:E->R^+, and asks...

All-Optical Label Switching (AOLS) is a new technology that performs packet forwarding without any optical–electrical–optical conversions. In this paper, we study the problem of routing a set of requests in AOLS networks using GMPLS technology, with the aim of minimizing the number of labels required to ensure the forwarding. We first formalize the...

In this paper, we address the problem of gathering information in one node (sink) of a radio network where interference constraints are present: when a node transmits, it produces interference in an area bigger than the area in which its message can actually be received. The network is modeled by a graph; a node is able to transmit one unit of info...

In this paper, we address the problem of computing the transport capacity of Wireless Mesh Networks (WMNs) dedicated to Internet access. Routing and transmission scheduling have a major impact on the capacity provided to the clients. A cross-layer optimization of these problems allows the routing to take into account contentions due to radio interf...

We study algorithmic and complexity issues originating from the problem of data gathering in wireless networks. We give an
algorithm to construct minimum makespan transmission schedules for data gathering when the communication graph G is a tree network, the interference range is any integer m ≥ 2, and no buffering is allowed at intermediate nodes....

Distributed and peer-to-peer storage systems are foreseen as an alternative to the traditional data centers and in-house backup solutions. In the past few years many peer-to-peer storage systems have been proposed. Most of them rely on the use of erasure codes to introduce redundancy to the data. This kind of system depends on many parameters that...

This paper studies the natural linear programming relaxation of the path coloring problem. We prove constructively that finding
an optimal fractional path coloring is Fixed Parameter Tractable (FPT), with the degree of the tree as parameter: the fractional
coloring of paths in a bounded degree trees can be done in a time which is linear in the size...

Peer-to-peer systems are foreseen as an efficient solution to achieve reliable data storage at low cost. To deal with common
P2P problems such as peer failures or churn, such systems encode the user data into redundant fragments and distribute them
among peers. The way they distribute it, known as placement policy, has a significant impact on their...

In this paper, we address the problem of bandwidth allocation and routing in wireless networks. A first model of this problem is known as the Round Weighting Problem (RWP) in which a weight is assigned to the set of rounds, i.e. a set of pairwise non-interfering links. We present a new formulation that forgets about the routing and concentrate on t...

In this work, we study the problem of routing packets between undifferentiated sources and sinks in a network modeled by a multigraph. We consider a distributed and local algorithm that transmits packets hop by hop in the network and study its behavior. At each step, a node transmits its queued packets to its neighbors in order to optimize a local...

Peer-to-peer systems are foreseen as an efficient solution to achieve reliable data storage at low cost. To deal with common P2P problems such as peer failures or churn, such systems encode the user data into redundant fragments and distribute them among peers. The way they distribute it, known as placement policy, has a significant impact on their...

We study two characteristics of a small-world graph proposed by Zhang et al. to model complex networks. Our study relies on the recursive structure of the graph. Firstly, we use it to design a labelling scheme in order to create an implicit routing (i.e., a routing scheme based on the label of vertices). Secondly, proving the average distance in th...

Large scale peer-to-peer systems are foreseen as a way to provide highly reliable data storage at low cost. To achieve high durability, such P2P systems encode the user data in a set of redundant fragments and distribute them among the peers. In this paper, we study the impact of different data placement strategies on the system performance when us...

Peer-to-peer storage systems aim to provide a reliable long-term storage at low cost. In such systems, peers fail continuously, hence, the necessity of self-repairing mechanisms to achieve high durability. In this paper, we propose and study analytical models that assess the bandwidth consumption and the probability to lose data of storage systems...

Traffic grooming is a central problem in optical networks. It refers to pack low rate signals into higher speed streams, in order to improve bandwidth utilization and reduce network cost. In WDM networks, the most accepted criterion is to minimize the number of electronic terminations, namely the number of SONET Add-Drop Multiplexers (ADMs). In thi...

All-Optical Label Switching (AOLS) is a new technology that performs packet forwarding without any Optical-Electrical-Optical (OEO) conversions. In this paper, we study the problem of routing a set of requests in AOLS networks using GMPLS technology, with the aim of minimizing the number of labels required to ensure the forwarding. We first formali...

All-Optical Label Switching (AOLS) is a new technology that performs forwarding without any Optical-Electrical-Optical conversions.
The most promising scheme to manage the control plane of these optical networks is Generic MultiProtocol Label Switching (GMPLS).
In this paper, we study the problem of routing a set of requests in GMPLS networks with...

Wireless mesh network performance issues have been modeled by the Joint Routing and Scheduling Problem (JRSP) in which a maximum per-flow throughput is computed.
A classical relaxation of JRSP, denoted as the Round Weighting Problem (RWP), consists in assigning enough weight to sets of compatible simultaneous transmissions (rounds), while minimizin...

In this paper, we address the routing and call scheduling problem in which one has to find a minimum-length schedule of selected links in a TDMA (time division multiple access) based wireless network. As we deal with multi-hop networks, these selected links represent a routing solution (paths) providing enough capacity to achieve the routers requir...

In this work, we study the problem of routing packets between undifferentiated sources and sinks in a network modeled by a multigraph. We provide a distributed and local algorithm that transmits packets hop by hop in the network and study its behaviour. At each step, a node transmits its queued packets to its neighbours in order to optimize a local...

Dans cet article, nous présentons et étudions des modèles analytiques de systèmes de stockage pair-à-pair fiables à long terme. Les pairs sont sujets à des pannes définitives (défaillance du disque, départ du pair) induisant la perte de toutes les données stockées par le pair. Ces pannes ont lieu en continu. Afin de pérenniser les données il est in...

All-Optical Label Switching (AOLS) is a new technology that performs packet forwarding without any Optical-Electrical-Optical (OEO) conversions. In this paper, we study the problem of routing a set of requests in AOLS networks using GMPLS technology, with the aim of minimizing the number of labels required to ensure the forwarding. We first formali...

In this paper, we present a result concerning the relation between the path-with of a planar graph and the path-width of its dual. More precisely, we prove that for a 3-connected planar graph G, pw(G) 3pw(G ) + 2. For 4-connected planar graphs, and more generally for Hamiltonian planar graphs, we prove a stronger bound pw(G ) 2 pw(G) + c. The best...

Given a graph G=(V,E) with |V|=n, we consider the following problem. Place m=n points on the vertices of G independently and uniformly at random. Once the points are placed, relocate them using a bijection from the points to the vertices that minimizes the maximum distance between the random place of the points and their target vertices. We look fo...

Un reseau $\plk$ est un graphe non oriente avec $p + \lambda$ entrees, $p + k$ sorties et des noeuds internes de degre $4$. Un reseau $\plk$ est valide si pour n'importe quel choix de $p$ entrees et de $p$ sorties il existe $p$ chemins aretes disjoints reliant les entrees aux sorties. Dans le cas particulier $\lambda = 0$, un reseau $\plk$ est un {...

We define and study an optimization problem that is motivated by bandwidth allocation in radio networks. Because radio transmissions are subject to interference constraints in radio networks, physical space is a common resource that the nodes have to share in such a way, that concurrent transmissions do not interfere. The bandwidth allocation probl...

In this paper we present a new upper bound on the approximation ratio of the Minimum Spanning Tree heuristic for the basic
problem on Ad-Hoc Networks given by the Minimum Energy Broadcast Routing (MEBR). We introduce a new analysis allowing to establish a 6.33-approximation ratio in the 2-dimensional case, thus decreasing
the previously known 7.6 u...

A general instance of a Degree-Constrained Subgraph problem consists of an edge-weighted or vertex-weighted graph G and the objective is to find an optimal weighted subgraph, subject to certain degree constraints on the vertices of the subgraph. This paper considers two natural Degree-Constrained Subgraph problems and studies their behavior in term...

In this paper we give exact or almost exact bounds for the continuous gathering problem on grids. Under very general hypothesis on the traffic demand, we mainly prove that the throughput is determined by the bottleneck around the base station. We deal with two cases: the base station located in the center and in the corner. We use dual lower bounds...

Un des problèmes au coeur de l'optimisation des réseaux radio maillés est le routage et l'ordonnancement d'appels. Dans cet article, nous étudions une relaxation classique de ce problème qui consiste à répartir la capacité entre les ensembles d'appels simultanés de manière à garantir un débit suffisant à chaque routeur du réseau. Nous introduisons...

In this paper we present new results on the performance of the Minimum Spanning Tree heuristic for the Minimum Energy Broadcast Routing (MEBR) problem. We first prove that, for any number of dimensions d≥2, the approximation ratio of the heuristic does not increase when the power attenuation coefficient α, that is the exponent to which the coverage...

The problem we consider originates from the design of effi- cient on-board networks in satellites (also called Traveling Wave Tube Amplifiers). Signals incoming in the network through ports have to be routed through an on-board network to amplifiers. The network is made of expensive switches with four links and subject to two types of con- straints...

This article investigates the consequences of the Shared Risk Ressource Groups (SRRG) model on classical combinatorial concepts of network survivability. It focuses on complexity and approximability issues, and on the evolutions of the relationships among these questions. We introduce a combinatorial model for SRRG based on edge-colored graphs. The...

Le groupage est un problème central dans l'étude des réseaux optiques. Dans cet article, on propose le premier résultat d'inapproximabilité pour le problème du groupage, en affirmant la conjecture de Chow et Lin (2004, Networks, 44, 194-202), selon laquelle le groupage est APX-complet. On étudie aussi une version amortie du problème de sous-graphe...

This article investigates complexity and approximability properties of combinatorial optimization problems yielded by the notion of Shared Risk Resource Group (SRRG). SRRG has been introduced in order to capture network survivability issues where a failure may break a whole set of resources, and has been formalized as colored graphs, where a set of...

In the broadcasting problem, one node needs to broadcast a message to all other nodes in a network. If nodes can only communicate with one neighbour at a time, broadcasting takes at least " log2 N# rounds in a network of N nodes. In the neigh- bourhood broadcasting problem, the node that is broadcasting only needs to inform its neighbours. In a bin...