Mascotte is a joint team between Inria Sophia Antipolis Méditerranée and the laboratory I3S (Informatique Signaux et Systèmes de Sophia Antipolis) which itself belongs to CNRS (Centre National de la Recherche Scientifique) and UNS (University of Nice Sophia Antipolis). Its research fields are Algorithmics, Discrete Mathematics, Combinatorial Optimization and Simulation, with applications to telecommunication networks.
The objectives of the Mascotte project-team are to design networks and communication algorithms. In order to meet these objectives, the team studies various theoretical tools, such as Discrete Mathematics, Graph Theory, or Algorithmics and develops applied techniques and tools, especially for Combinatorial Optimization and Computer Simulation. In particular Mascotte used in the last years both these theoretical and applied tools for the design of various networks, such as WDM, wireless (radio), satellite, overlay, and peer-to-peer networks. This research has been done within various industrial and international collaborations.
This results also in the production of advanced softwares such as Grph and DRMSim, and in the contribution to large open source softwares such as SageMath.
The project develops tools and theory in the following domains: Discrete Mathematics (in particular Graph Theory), Algorithmics, Combinatorial Optimization and Simulation.
Typically, a telecommunication network (or an interconnection
network) is modeled by a graph. A vertex may represent either a
processor or a router or any of the following: a switch, a radio
device, a site or a person. An edge (or arc) corresponds to a
connection between the elements represented by the vertices (logical
or physical connection). We can associate more information both to
the vertices (for example what kind of switch is used, optical or
not, number of ports, equipment cost) and to the edges (weights
which might correspond to length, cost, bandwidth, capacity) or
colors (modeling either wavelengths or frequencies or failures) etc.
Depending on the application, various models can be defined and have
to be specified. This modeling part is an important task. To solve
the problems, we manage, when possible, to find polynomial
algorithms. For example, a maximum set of disjoint paths between two
given vertices is by Menger's theorem equal to the minimum
cardinality of a cut. This problem can be solved in polynomial time
using graph theoretic tools or flow theory or linear programming. On
the contrary, determining whether in a directed graph there exists a
pair of disjoint paths, one from
Graph coloring is an example of concept which appears in various contexts: WDM networks where colors represent wavelengths, radio networks where colors represent frequencies, fault tolerance where colors represent shared risk resource groups, and scheduling problems. Another tool concerns the development of new algorithmic aspects like parameterized algorithms.
In the last year the main application domain of the project remained Telecommunications. Within this domain, we consider applications that follow the needs and interests of our industrial partners, in particular Orange Labs or Alcatel-Lucent Bell-Labs, but also SMEs like 3-Roam and Avisto .
Mascotte is mainly interested in the design and management of heterogeneous networks. The project has kept working on the design of backbone networks (optical networks, radio networks, IP networks).
The project has also been working on routing algorithms such as dynamic and compact routing schemes in the context of the FP7 EULER leaded by Alcatel-Lucent Bell-Labs (Belgium). It also studied the evolution of the routing in case of any kind of topological modifications (maintenance operations, failures, capacity variations, etc.). Finally, an emphasis is done on green networks with low power consumption. This work is in collaboration with Orange Labs and the SME 3-Roam and partly supported by the ANR DIMAGREEN.
Around 20,000 lines of code, developed in Java.
The objective of Grph is to provide researchers and engineers a suitable graph library for graph algorithms experimentation and network simulation. Grph is primarily a software library, but it also comes with a set of executable files for user interaction and graph format conversion; as such, it can be used autonomously. Performance and accessibility are the primary targets of the Grph library. It allows manipulating large graphs (millions of nodes). Its model considers mixed graphs composed of directed and undirected simple- and hyper-edges. Grph comes with a collection of base graph algorithms which are regularly augmented.
So far, known users of the Grph library include people at Mascotte and others involved in the FP7 EULER project. It got some contribution from the Inria team GANG who contributed Grph with an implementation of the four-sweep algorithm which provides accurate lower bound on the diameter in linear time. It has a number of other academic users including research students at Bergamo University (Italy), and University of Southern Denmark (students supervised by Jørgen Bang-Jensen).
Grph includes bridges to other graph libraries such as JUNG, JGraphT, CORESE (a software developed by the WIMMICS team Inria-I3S), LAD (Christine Solnon, LIRIS), Nauty (Brendan D. McKay), as well as specific algorithms developed by Matthieu Latapy and Jean-Lou Guillaume (LIP6), etc.
Grph is distributed under the terms of a license defined by its
contributors and is available for download. This license allows free
usage and access to the source code. See
http://
In 2012, numerous graph algorithms have been added to Grph, such as maximum matching, minimum vertex cover (brute force, branching, Niedermeier), maximum independent set (Fomin/Grandoni/Kratsch). Furthermore, to answer a number of issues about the generation of graph instances with particular properties, a framework for evolutionary computing dedicated to graphs was integrated to Grph. Moreover, a reworked version of Mascsim was integrated in Grph.
On-going works concern the distributed execution of graph algorithms, and a bridge to Sage.
See also the web page http://
Around 45,000 lines, developed in Java, collaboration between MASCOTTE and LaBRI.
DRMSim relies on a discrete-event simulation engine aiming at enabling the large-scale simulations of routing models. DRMSim is developped in the framework of the FP7 EULER project . It proposes a general routing model which accommodates any network configuration. Aside to this, it includes specific models for Generalized Linear Preference (GLP), and k-chordal network topologies, as well as implementations of routing protocols, including the routing protocol proposed in and lightweight versions of BGP (Border Gateway Protocol).
The system model considers the dynamic evolution of the simulated network. This model takes as its input parameter the distribution of failure probability for both routers and links.
The metric model takes measures along a discrete-event simulation which can be performed in many ways.
Commonly, a simulation campaign consists in iterating over the set of combinations of parameter values, calling the simulation function for every combination. These combinations are most often complex, impeding there description by a set of mathematical functions. Thus DRMSim provides a simulation methodology that describes (programmatically) the way a simulation campaign should be conducted.
DRMSim stores on disk every step of the execution of a simulation campaign. In a simulation campaign, simulation runs are independent (no simulation depends on the result computed by another simulation). Consequently they can be executed in parallel. Because one simulation is most likely to use large amount of memory and to be multi-threaded, parallelizing the simulation campaign on one single computer is a poor parallelization scheme. Instead, we currently work at enabling the remote parallel execution of several simulation runs, with the same distribution framework that is used in the Grph library.
DRMSim relies on the Mascsim abstract discrete-event simulation framework, the Grph library and the Java4Unix integration framework.
Finally, from an object-oriented point of view of its conception model, DRMSim manipulates graph abstractions, allowing the user to force the use of a library different from the default one, i.e. Grph.
See also the web page http://
Developed in Python, Cython, and C++. Mascotte members have already contributed to the development of more than 180 patches and to the reviewing process of more than 200 patches that are now part of the standard distribution.
Sagemath is a free open-source mathematics software aiming at becoming an alternative to Maple and Matlab. Initially created by William Stein (Professor of mathematics at Washington University), Sagemath is currently developed by more than 180 contributors around the world (mostly researchers) and its source code has reached 350 MB. It is of interest for Mascotte members because it combines a large collection of graph algorithms with various libraries in algebra, calculus, combinatorics, linear programming, statistics, etc.
We use Sagemath for quickly testing algorithms, analyzing graphs, and disseminating algorithms. We also use it for teaching purposes in the Master IFI, stream UBINET.
In 2012, David Coudert has contributed to the development of the Sage releases 5.0 to 5.6 with 15 patches (from bug fix to advance graph algorithms) and participated to the reviewing process of more than 30 patches.
More than 5,000 lines, developed in Java.
Java4unix proposes a development and distribution framework which simplifies the use of Java for UNIX software programming/distribution. Until now, Java could hardly be used for the development UNIX applications because invoking Java applications from the UNIX shell must be done through an explicit call to the Java virtual machine and writing simple things in Java often requires long coding. Java4unix aims at filling those two gaps by providing a UNIX installer for java applications, turning them to standard UNIX application and a framework that UNIX programmers may use to manipulate files/text, etc.
Java4unix includes a module which enables the reporting and automatic releasing of Eclipse Java projects.
See also the web page
http://
Developed in Java.
Jalinopt is a Java toolkit for building and solving linear programs. It consists of a straightforward object-oriented model for linear programs, as well as a bridge to most common solvers, including GLPK and CPLEX. It is an interface to many LP solvers allowing users to code independently of the solver effectively. Altought Jalinopt is inspired by Mascopt and JavaILP, it provides a significantly different model and an utterly different approach to connecting to the solver. In particular this approach, based in inter-process piping, offers better portability, and the possibility to connect (via SSH) to solvers on remote computers.
In 2012, we refined the object-oriented model of Jalinopt and improved its portability by making it working with LPSolve as its default native solver.
See also the web page
http://
More than 1,500 lines, developed in Java.
JavaFarm is a middleware enabling the distribution of Java applications across farms of servers.
Its workflow basically enables an application to locally aggregate code and data into an object, called job, that will migrate to another computer where it will be computed. When a job completes, its result is transferred back to the caller. Among other features, JavaFarm supports futures (asynchronous job executions), thereby enabling parallelization of the distributed code. The design objectives of JavaFarm are to make distribution and parallelism as transparent and easy as possible.
See also the web page
http://
Around 12,000 lines, developed in Java.
Mascsim is a distributed discrete event simulator whose main target is to be easy to use. Unlike most discrete-event simulators, the researcher who is using Mascsim is required to provide only the bare minimum material needed for the simulation: a model for the system, a set of events describing what is going on in the system, as well as a set of metrics of interest. The simulation process is then entirely automatized.
In 2012, Mascsim was adapted and integrated to Grph.
See also the web page
http://
Around 12,000 lines, developed in Python.
P2PVSim is a simple discrete-event simulator created for analyzing theoretical properties of peer-to-peer live video streaming algorithms. Implemented in Python it was designed with clarity and extensibility in mind from the beginning. It is capable of simulating overlays of a few thousands of peers. Multiple control protocols have been implemented. At the same time, a lot of work was put into the performance and scalability aspects of the software. Currently it is meant for simulating overlays of a few thousand peers running multiple control protocols that have been implemented.
In 2012, a distributed version of P2PVSim was developed. The objectives for developing a distributed version was to fasten the simulation of large campaigns, that would be too long to run on one single computer. The distributed P2PVSim runs on an arbitrary number of computers. It has been so far used with success on a dozen computers with multiple cores all located in the same LAN.
Network design is a very wide subject that concerns all kinds of networks. We mainly study telecommunications networks which can be either physical networks (backbone, access, wireless, ...) or virtual (logical) ones. The objective is to design a network able to route a (given, estimated, dynamic, ...) traffic under some constraints (e.g. capacity) and with some quality of service (QoS) requirements. Usually the traffic is expressed as a family of requests with parameters attached to them. In order to satisfy these requests, we need to find one (or many) path(s) between their end nodes. The set of paths is chosen according to the technology, the protocol or the QoS constraints. The design can be done at the conception of the network (i.e. when conceiving a virtual network in MPLS where we have to establish virtual paths) or to adapt the network to changes (failures, new link, updates of routers, variation of traffic, ...). Finally there are various optimization criteria which differ according to the point of view: for a network user they are related to his/her satisfaction (minimizing delays, increasing available bandwidth, ...), while for a network operator, economics criteria like minimizing deployment and operating costs are more important.
This very wide topic is addressed by a lot of academic and industrial teams in the world. Our approach is to attack these problems with tools from Discrete Mathematics.
All-Optical Label Switching (AOLS) is a promising technology that performs packet forwarding without any optical-electrical-optical conversions, thus speeding up the forwarding. However, the cost of this technology requires limiting the number of labels needed to ensure the forwarding when routing a set of requests using GMPLS technology. In particular, this prevents the usage of label swapping techniques.
We have studied the routing problem in this context using label
stacking techniques. We have formalized the problem by associating to
each routing strategy a logical hypergraph, called a hypergraph
layout, whose hyperarcs are dipaths of the physical graph, called
tunnels in GMPLS terminology. We defined a cost function for the
hypergraph layout, depending on its total length plus its total hop
count. Minimizing the cost of the design of an AOLS network can
then be expressed as finding a minimum cost hypergraph layout.
In , we prove hardness results for the problem. On
the other hand, we provide approximation algorithms, in particular an
IP multicast is a protocol that deals with group communications with the aim of reducing traffic redundancy in the network. However, due to difficulty in deployment and poor scalability with a large number of multicast groups, IP multicast is still not widely deployed nor used on the Internet. Recently, Xcast6 and Xcast6 Treemap, two network layer multicast protocols, have been proposed with complementary scaling properties to IP multicast: they support a very large number of active multicast sessions. However, the key limitation of these protocols is that they only support small multicast groups. To overcome this limitation, we have proposed the Xcast6 Treemap Island , , a hybrid model of Application Layer Multicast (ALM) and Xcast6 that can work for large multicast groups. We have shown the feasibility of our model by simulation and comparison with IP multicast and NICE protocols.
Congestion control is a distributed algorithm to share network bandwidth among competing users on the Internet. In the common case, quick response time for mice traffic (http traffic) is desired when mixed with elephant traffic (ftp traffic). The current approach using loss-based with Additive Increase, Multiplicative Decrease (AIMD) is too greedy and eventually, most of the network bandwidth would be consumed by elephant traffic. As a result, it causes longer response time for mice traffic because there is no room left at the routers. MaxNet is a new TCP congestion control architecture using an explicit signal to control transmission rate at the source node. In , we show that MaxNet can control well the queue length at routers and therefore the response time to http traffic is several times faster than with TCP Reno/RED.
The notion of Shared Risk Link Group, SRLG has been introduced to capture multiple correlated failures in a network. A SRLG is a set of links that fail simultaneously if a given event (risk) occurs. In such multiple failures scenario, the problem of Diverse Routing consists in finding two SRLG-disjoint paths between a pair of nodes. We consider in , such problem for localized failures, when all the links of a SRLG verify the star property i.e. when they are incident to the same node. We prove that in this case the problem is in general NP-complete and determine some polynomial cases.
We study the problem of gathering information from the nodes of a
radio network into a central node. We model the network of possible
transmissions by a graph and consider a binary model of interference
in which two transmissions interfere if the distance in the graph
from the sender of one transmission to the receiver of the other is
Other results on multi-interface networks were obtained outside of Mascotte , , .
The problem of finding and updating shortest paths in distributed networks is considered crucial in today's practical applications. In the recent past, there has been a renewed interest in designing new efficient distance-vector algorithms (e.g., the distributed Bellman-Ford method implemented in the routing information protocol, RIP) as an alternative to link-state solutions (e.g., open shortest path first, OSPF) for large-scale distributed networks such as the autonomous systems topology of the Internet.
This year, we have proposed a new loop-free distance-vector routing algorithm, called LFR (Loop Free Routing), which is able to update the shortest paths of a distributed network with
We then proposed a new technique, called Distributed Computation Pruning (DCP) , for reducing the total number of messages sent and the space occupancy per node of every distance-vector routing algorithm based on shortest paths. We have evaluated experimentally the combination of DCP with DUAL and with LFR. We have observed that these combinations lead to a significant gain both in terms of number of messages sent and memory requirements per node.
We have also considered routing problems arising in road networs. In particular, we have conducted a theoretical study of the graph-augmentation problem of adding shortcuts in order to speedup route planning techniques . We studied the algorithmic complexity of the problem and proposed approximation algorithms for a special graph class. We have also investigated ILP-based exact approaches and show how to stochastically evaluate a given shortcut assignment on graphs that are too large to do so exactly.
With the constant increase of the number of routing entries in the Internet, the size of the routing tables stored at router nodes increases drastically. Routing schemes such as BGP are showing their limits in terms of update time, search time, cost of signaling, etc. and alternatives have to be proposed. In particular, compact routing schemes propose interesting trade-offs between the size of the routing tables and the quality of the routes. They also take advantage of the particular properties arising in large scale networks such as low (logarithmic) diameter and high clustering coefficient.
High clustering coefficient implies the existence of few large induced cycles. Considering this fact, we proposed in a routing scheme that computes short routes in the class of
We also used cops-and-robber games (See Section ) to propose the first compact routing scheme for
In addition, we have pursued our investigation of the kind of structural graph properties that can or cannot be deduced from local (partial) views of the network. Such knowledge is crucial for the design of routing schemes. To this end, we have exhibited a hierarchy of problems and distributed models of computation .
The evaluation of new routing models asks for large-scale and intensive simulations. However, existing routing models simulators such as DRMSim are limited in terms of the number of routing table entries it can dynamically process and control on a single computer. Therefore, we have conducted a feasibility study of the extension of DRMSim so as to support the Distributed Parallel Discrete Event paradigm . We have studied several distribution models and their associated communication overhead. We have in particular evaluated the expected additional time (in hours) required by a distributed simulation of BGP (border gate protocol), the current interdomain routing protocol of the Internet, compared to its sequential simulation. We show that such a distributed simulation of BGP is possible with a reasonable time overhead.
In production networks, traffic evolution, failures and maintenance operations force to adapt regularly the current configuration of the network (virtual topology, routing of connections). The routing reconfiguration problem in WDM networks consists of scheduling the migration of established lightpaths from current routing to a new pre-computed one while minimizing service disruptions. We have shown in the past the relations between this problem and the graph searching problem and established NP-completeness and inapproximability results.
This year, we proved the monotonicity of the process strategy game , the graph searching game modeling the routing reconfiguration problem. Then, we have investigated on the influence of physical layer impairment constraints on the reconfiguration problem . Setting up a new wavelength in a fiber of a WDM network requires recalibrating the other wavelengths passing through this fiber. This induces a cost (e.g., time, energy, degradation of QoS) that depends nonlinearly on the number of wavelengths using the fiber. Therefore, the order in which requests are switched affects the total cost of the operation. We have studied the corresponding optimization problem by modeling the cost of switching a request as a non-linear function depending on the load of the links used by the new lightpath. We have proved that determining the optimal rerouting order is NP-complete for a 2-nodes network, established general lower and upper bounds, identified classes of instances where the problem can be solved in polynomial time, and proposed a heuristic algorithm.
Recently, energy-aware routing has gained increasing popularity in the networking research community. The idea is that traffic demands are aggregated over a subset of the network links, allowing other links to be turned off to save energy. We develop several methods to improve routing protocols for backbone, wireless and content delivery networks. Several studies exhibit that the traffic load of the routers only has a small influence on their energy consumption. Hence, the power consumption in networks is strongly related to the number of active network elements, such as interfaces, line cards, base chassis,... The goal thus is to find a routing that minimizes the (weighted) number of active network elements used when routing. In , we exhibit that the power consumption can be reduced of approximately 33 MWh for a medium-sized backbone network.
In , we propose GreenRE - a new energy-aware routing model with the support of the new technique of data redundancy elimination (RE). Based on real experiments on Orange Labs platform and on simulations on several network topologies, we show that GreenRE can gain further 30% energy savings in comparison with the traditional energy-aware routing model.
One of the new challenges facing research in wireless networks is the design of algorithms and protocols that are energy aware. In , we use for the first time the evolving graph combinatorial model as a tool to prove an NP-Completeness result, namely that computing a Minimum Spanning Tree of a planar network in the presence of mobility is actually NP-Complete.
Recently, there is a trend to introduce content caches as an inherent capacity of network equipment, with the objective of improving the efficiency of content distribution and reducing network congestion. In , we study the impact of using in-network caches and CDN cooperation on an energy-efficient routing: up to 23% of power can be saved in the backbone this way.
In , we study the energy efficiency of the networking part of data centers, accounting for between 10-20% of the total power consumption. We proposed a novel approach, called VMPlanner, for power reduction in the virtualization-based data centers. The idea of VMPlanner is to optimize both virtual machine placement and traffic flow routing so as to turn off as many unneeded network elements as possible for power saving.
Finally, in , , we summarize the main research results of the last years for energy efficiency for backbone, wireless, cellular and content distribution networks and highlight the main challenges of the field. Results are given for two operator networks, considering power and traffic forecasts for 2020.
Mascotte is also interested in the algorithmic aspects of Graph Theory. In general we try to find the most efficient algorithms to solve various problems of Graph Theory and telecommunication networks.
We used graph theory to model various networks' problems. In general we study their complexity and then we investigate the structural properties of graphs that make these problems hard or easy. In particular, we try to find the most efficient algorithms to solve the problems, sometimes focusing on specific graph classes where the problems are polynomial-time solvable.
Degree Constraint Subgraphs. A natural question in current social networks is How do one find a small community (subgraph) in which anyone as at least
Hyperbolicity in Large graphs. Hyperbolicity is a geometric notion that measure how the various shortest paths connecting two vertices can diverge in a graph. Knowing its value provides information on the geometry of the network, moreover it has practical implications for shortest path routing. Hyperbolicity can be
computed in polynomial time algorithm (
Hull Number of graphs. In , we study the (geodesic) hull number of graphs. For any two vertices
Pursuit-evasion encompasses a wide variety of combinatorial problems related to the capture of a fugitive residing in a network by a team of searchers. The goal consists in minimizing the number of searchers required to capture the fugitive in a network and in computing the corresponding capture strategy. This can also be viewed as cleaning the edges of a contaminated graph. We investigated several variants of these games.
Web Caching & the surfer Game. A surprising application of some variant of pursuit-evasion games (namely Cops and Robber games) is the problem for a web-browser to download documents in advance while an internaut is surfing on the Web. In , , we provide a modelling of the prefetching problem in terms of Cops and Robber games. The parameter to be optimized is then the download-speed necessary for the Internaut only accesses to already download webpages. This allows us to provide several complexity results and polynomial-time algorithms in some graph classes.
Connected Graph Searching. Another variant of pursuit-evasion games is graph searching which is mainly related to graph decompositions. For instance, the minimum number of searchers needed to capture an invisble fugitive in a graph is equal to its pathwidth plus one. In , we investigated the connected variant of this game. A strategy is called connected if the clear part (the part where the fugitive cannot stand) always induces a connected subgraph. The main motivation for studying connected graph searching is the design of distributed protocols allowing searchers to compute a capture strategy (see also Section ). gathers most of the results of the last decade concerning connected graph searching, mainly focussing on the cost of connectivity in terms of number of searchers.
We investigated algorithmic problems arising in complex networks like the Internet or social networks. In this kind of networks, problems are becoming harder or impracticable because of the size and the dynamicity of these networks. One way to handle the dynamicity is to provide (distributed) fault tolerant algorithms. Studying the mobile agents paradigm seems to be a promissing approach (somehow related to Cops and Robber in Section ) to adress some models of distributed computing. We considered distributed or even self-stabilizing algoritms for gathering and graph searching problems.
Graph Searching and Routing Reconfiguration. In , we developed a generic distributed algorithm for computing and updating various parameters on trees including the process number (see Section ), and other related graph searching parameters (see Section ). We also proposed an incremental version of the algorithm allowing to update these parameters after addition or deletion of any tree edge.
Robots in anonymous networks. Motivated by the understanding of the limits of distributed computing, we consider a recent model of robot-based computing which makes use of identical, memoryless mobile robots placed on nodes of anonymous graphs. The robots operate in Look-Compute-Move cycles that are performed asynchronously for each robot. In particular, we consider various problems such as graph exploration, graph searching and gathering in various graph classes. We provide a new distributed approach which turns out to be very interesting as it neither completely falls into symmetry-breaking nor into symmetry-preserving techniques. More precisely, we design algorithms for the gathering in rings , , grid and trees . We also proposed a general approach to solve the three problems in rings. Finally, in , , , algorithms are designed to solve the graph searching problem in trees.
Graph theory can be roughly partitioned into two branches: the areas
of undirected graphs and directed graphs (digraphs). Even though
both areas have numerous important applications, for various
reasons, undirected graphs have been studied much more extensively
than directed graphs. One of the reasons is that many problems for digraphs are much more difficult than
their analogues for directed graphs. For example, one of
the cornerstones of modern (undirected) graph theory is Minor
Theory of Robertson and Seymour. Unfortunately, we cannot expect an equivalent for directed graphs.
Minor Theory implies in particular that,
for any fixed
In a directed graph, a star is an arborescence with at least one arc, in which the root dominates all the other vertices. A galaxy is a vertex-disjoint union of stars. In , we consider the Spanning Galaxy problem of deciding whether a digraph
Hypergraphs are a generalization of graphs, in which every edge is incident to a set of vertices of any size (not necessarily 2). Like for digraphs, a lot fewer is known about them than about graphs. The two notions of eulerian and hamoltinians cycles have been extensively studied for graphs and digraphs. The analogue notion of eulerian cycle in a hypergraph was only introduced in 2010 by Lonc and Naroski. In , we introduce the notions of eulerian and hamiltonian circuits in directed hypergraphs. We show that both associated decision problems are NP-complete. Some necessary conditions for a dihypergraph to be have an eulerian circuit are presented. We exhibit some families of hypergraphs for which those are sufficient conditions. We also generalize a part of the properties of eulerian digraphs to the uniform and regular directed hypergraphs. Finally, we show that the de Bruijn and Kautz dihypergraphs are eulerian and hamiltonian in most cases.
We mainly study graph colouring problems that model channel assignment problems.
A well-known such general problem is the following: we are given a graph
We mainly studied a particular, yet quite general, case, called backbone colouring, in which there are only two levels of interference. So we are given a graph
Another meaningful and very well-studied particular case of backbone colouring is
In , we studied another colouring problem motivated by a practical frequency assignment problem and, up to our best knowledge, new. In wireless networks, a node interferes with other nodes, the level of interference depending on numerous parameters: distance between the nodes, geographical topography, obstacles,... We model this with a weighted graph
Since some of the channel assignment problems must be done on-line,
we are interested in some on-line graph colouring heuristics. We only studied such heuristics for the classical proper colouring.
The easiest one, and the most widespread one, is the greedy algorithm, which colours the vertices one after another, giving to each vertex the smallest possible positive integer that is not already used by one of its neighbours.
The Grundy number of a graph
A colouring
Many more results on greedy colourings and
We studied other variations of graph colouring.
In , we aim at characterizing the class of graphs that admit a good edge-labelling. Such graphs are
interesting, as they correspond to set of requests in UPP-digraphs (in which there is at most one dipath
from a vertex to another) for which the minimum number of wavelengths is equal to the maximum load. This
implies that the problem can be solved efficiently. First, we exhibit infinite families of graphs for which no
good edge-labelling can be found. We then show that deciding if a graph admits a good edge-labelling is
NP-complete. Finally, we give large classes of graphs admitting a good edge-labelling:
For a connected graph
On Wireless IP Service Deployment optimization and monitoring.
"Convention de recherche encadrant une bourse CIFRE" on the topic Outils algorithmiques pour la détection des communautés.
"Convention de recherche encadrant une bourse CIFRE" on the topic Smart Transports: optimisation du trafic dans les villes.
"Convention de recherche encadrant une bourse CIFRE" on the topic Graphic Processing Units for Signal Processing with joint supervision with Aoste project.
The objectives of the project DIMAGREEN (DesIgn and MAnagement of GREEN networks with low power consumption) are to introduce and analyze energy-aware network designs and managements in order to increase the life-span of telecommunication hardware and to reduce the energy consumption together with the electricity bill.
(http://
The project AGAPE (Parameterized and exact graph algorithms) is led by Mascotte and implies also LIRMM (Montpellier) and LIFO (Orléans). The aim of AGAPE is to develop new techniques to solve exactly NP- hard problems on graphs. To do so, we envisage two approaches which are closely related ways to reduce the combinatorial explosion of NP-hard problems: moderately exponential exact algorithms and fixed-parameter tractability.
The ECOSCells (Efficient Cooperating Small Cells) project aims at developing the algorithms and solutions required to allow Small Cells Network (SCN) deployment. The consortium gathers industrial groups, together with 3 SMEs and 6 research institutes: Alcatel-Lucent Bell Labs (leader), Orange Labs, 3-ROAM, Sequans, Siradel, Inria teams Maestro, Mascotte and Swing, Université d'Avignon et des Pays de Vaucluse, Laboratoire des Signaux et Systèmes / Supelec, LAAS and Eurecom.
(http://
Réseaux de communications, working group of GDR ASR, CNRS.
Action Graphes, working group of GDR IM, CNRS.
Title: EULER (Experimental UpdateLess Evolutive Routing)
Type: COOPERATION (ICT)
Defi: Future Internet Experimental Facility and Experimentally-driven Research
Instrument: Specific Targeted Research Project (STREP)
Duration: October 2010 - September 2013
Coordinator: ALCATEL-LUCENT (Belgium)
Others partners:
Alcatel-Lucent Bell, Antwerpen, Belgium
3 projects from Inria: CEPAGE, GANG and MASCOTTE, France
Interdisciplinary Institute for Broadband Technology (IBBT),Belgium
Laboratoire d'Informatique de Paris 6 (LIP6), Université Pierre Marie Curie (UPMC), France
Department of Mathematical Engineering (INMA) Université Catholique de Louvain, Belgium
RACTI, Research Academic Computer Technology Institute University of Patras, Greece
CAT, Catalan Consortium: Universitat Politecnica de Catalunya, Barcelona and University of Girona, Spain
Abstract: STREP EULER (Experimental UpdateLess Evolutive Routing) is part of FIRE (Future Internet Research and Experimentation) objective of FP7. It aims at finding new paradigms to design, develop, and validate experimentally a distributed and dynamic routing scheme suitable for the future Internet and its evolution. The STREP EULER gathers 7 partners: Alcatel-Lucent Bell (leader) (Antwerp, Belgique), IBBT (Ghent, Belgium), UCL (Louvain, Belgium), RACTI (Patras, Grece), UPC (Barcelona, Spain), UPMC (ComplexNetworks, Paris 6), Inria (MASCOTTE, GANG, CEPAGE). MASCOTTE is the leader of WP3 on Topology Modelling and Routing scheme experimental analysis.
Bilateral collaboration funded by the french CNRS. The funding covers scientific visits and workshops.
On Graph coloring: theoretical and algorithmic aspects.
Bilateral collaboration funded by the french ministry of foreign affairs (MAE), the french ministry of research and education (MESR), and the Deutscher Akademischer Austauschdienst (DAAD). The funding covers scientific visits.
"Défis algorithmiques dans les réseaux de communication". The purpose of the project is to exchange expertise between the discrete optimization group of RWTH Aachen University and the MASCOTTE team at Inria Sophia-Antipolis and to address algorithmic problems in communication networks.
GRATEL (Graphs and Telecomunications) has been started in collaboration with LABRI Bordeaux, UJF Grenoble and three partners in Taiwan: Sun Yat-sen University, the National Taiwan University and Academia Sinica.
ALERTE (ALgorithmes Efficaces pour les Réseaux de TElécommunications), with Pargo Team, Universidade Federal do Ceará, Brazil, accepted in June 2011.
University of Southern Denmark, Odensee, Denmark, May 1-31, 2012 (1 month);
Université Bordeaux 1, Bordeaux, France, May 21-25, 2012 (1 week);
JAIST, School of Information Science, Ishikawa, Japan, March 5-23, last week of June, September 12 - 30, 2012 (2 months);
University of L'Aquila, Italy, June 18 - July 13 (3 weeks);
Simon Fraser University, Vancouver, Canada, May 19-27, 2012 (1 week);
Concordia University, Montréal, Canada, April 23 - May 5, 2012 (3 weeks);
University of Oran, Algeria, April 22 - 28, November 21-28, 2012 (2 weeks);
Tokyo Woman's Christian University, Suginami-ku, Tokyo, Japan, March 19-29 (2 weeks);
Fluminense Federal University, Brazil, July 13-30, 2012 (3 weeks);
University of Oran, Algeria, October 16 - November 16, 2012 (1 month);
RWTH Aachen University, Germany, December 16-21, 2012 (1 week);
Abbotsford and SFU, Vancouver, Canada, March 1 - April 20, 2012 (1 month 1/2).
Orsay (March 23, 2012); Athens (May 20-29, 2012);
FUN Team, Inria Lille Nord Europe (July 1-6, 2012); Mathematics departement of RWTH Aachen, Germany (July 29-August 5, 2012);
Alcatel-Lucent Bell labs, Antwerpeen, Belgium (January 10-12, 2012); Mathematics departement of RWTH Aachen, Germany (July 24-27, 2012);
LIP, ENS Lyon (January 23-27, 2012);
LIP, ENS Lyon (January 23-27, 2012); Federal University of Ceara, Brasil (April 21-28, 2012); LABRI, University of Bordeaux 1 (July 9-11 2012);
LABRI, University of Bordeaux 1 (March 5-7, 2012);
LIP, ENS Lyon (January 23-27, 2012); LIF, Univ. Marseille (February 20-22, 2012); LRI, Univ. Paris-Sud 11 (March 19-20, 2012); Adolfo Ibanez University, Santiago, Chile (August 4-20, 2012);
Mathematics departement of RWTH Aachen, Aachen, Germany (August 26 -September 01, October 14 - December 06, 2012);
LABRI, University of Bordeaux 1 (March 5-10, 2012).
Expert for DRTT, and various projects outside France (Canada, Italy,...); Member of the Ph.D. committee of the University of Marseille;
Member of the comité du suivi doctoral of Inria Sophia Antipolis (since January 2009); Member of comité de sélection 27e section of UJF, Grenoble, 2012; Member of the scientific board of the GIS ENSL-UNS (CNRS, ENSL, Inria, UNS) since 2011; Expert for the National Sciences and Engineering Research Council of Canada (NSERC), the Future and Emerging Technologies Open Scheme (FET-Open) European program, and the ANR;
Member of the comité de sélection 27e section of University of Versailles St-Quentin; Member of the CDL (Commission for software development) at Inria Sophia Antipolis since 2009; Member of the Conseil de Département (Department Committee) of IUT Nice since 2007;
Member of the commission ad-hoc ATER 27 UNS, IUT PAST 27 and ATER 11; Member of Comité Permanent de Ressources Humaines (CPRH) UNS 27e; Member of the Conseil de Département (Department Committee) of IUT Nice; Expert for DRTT PACA.
Combinatorics Probability and Computing, Computer Science Reviews, Discrete Mathematics, Discrete Applied Mathematics, Journal of Graph Theory, Journal of Interconnection Networks (Advisory Board), Mathématiques et Sciences Humaines, Networks, Parallel Processing Letters, SIAM book series on Discrete Mathematics, Transactions on Network Optimization and Control, Discrete Mathematics, Algorithms and Applications;
Discrete Applied Mathematics (Elsevier); Networks (Wiley);
Discrete Mathematics and Theoretical Computer Science.
Pôle ResCom du GDR ASR du CNRS (since 2005); Rencontres francophones sur les aspects algorithmiques des télécommunications (AlgoTel);
Journées Graphes et Algorithmes (JGA); Journées Combinatoires et Algorithmes du Littoral Méditerranéen (JCALM).
11èmes Journées Combinatoire et Algorithmes du Littoral Méditerranéen, Sophia Antipolis, France (February 16-17, 2012). Organizers: J. Araujo, F. Havet, A. Kodjo, A. Lancin, L. Sampaio;
10th Journées du Pôle ResCom du GDR ASR, Paris, France (November 28-29, 2012). Organizer: C. Caillouet (co-chair).
Workshop Franco-brésilien de Graphes et Optimisation Combinatoire, Redonda, Brasil, April 16-20, 2012. Organizers: F. Havet (co-chair), J. Araujo, A.-K. Maia, L. Sampaio and R. Soares.
6th International Conference on FUN with Algorithms, Venice, Italy (June 4-6, 2012);
11th International Symposium on Experimental Algorithms (SEA'12), Bordeaux, France (June 7-9, 2012); IEEE GLOBECOM – Track on Green Communication Systems and Networks, Anaheim, CA, USA (December 3-7, 2012);
14emes Journées Graphes et Algorithmes (JGA 2012);
14e Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (Algotel’12), La Grande Motte, France, May 29- June 1st, 2012.
Presentation on Energy efficiency in backbone and backhaul networks at Journées du pôle Systèmes de Communications Sécurisées, Sophia Antipolis, January 24, 2012;
Workshop Franco-brésilien de Graphes et Optimisation Combinatoire, Redonda, Brazil (April 16-20, 2012);
Birmingham workshop on Probabilistic methods in Graph theory, Birmingham, U. K. (March 25-29, 2012); Workshop Franco-brésilien de Graphes et Optimisation Combinatoire, Redonda, Brazil (April 16-20); SIAM Discrete Mathematics Conference, Halifax, Canada (June 18-21, 2012); Bordeaux Graph Workshop, Bordeaux, France (November 21-24, 2012) (Plenary Speaker);
GRASTA'12, Banff, Canada (October 8-12, 2012); IMSA seminar, Univ. Adolfo Ibanez, Santiago, Chile (August 10th, 2012).
first meeting of GT Complexité et Algorithmes, Paris (November 21-22, 2012). Attended by N. Nisse and S. Pérennes;
First year review meeting, Bruxelles, Belgium (January 13, 2012). Attended by A. Lancin, D.Coudert; WP2 technical meeting, Bordeaux, France (March 8-9, 2012). Attended by A. Lancin, B. Li, N. Nisse; Plenary meeting and Technical Advisory Board meeting, Ghent, Belgium (June 5-8, 2012). Attended by D. Coudert, A. Lancin, and N. Nisse; 2nd year review meeting, Sophia Antipolis, France (October 19, 2012). Attended by D. Coudert, A. Lancin, and N. Nisse; Plenary meeting and Technical Advisory Board meeting, Louvain-la-Neuve, Belgium (December 10-12, 2012). Attended by A. Lancin and N. Nisse;
Evaluation of the Mascotte project-team at the evaluation seminar of the research theme Networks and Telecommunications of Inria, Paris, France (March 21-23, 2012). Attended by most of the MASCOTTE permanent members (speakers: D. Coudert, F. Havet, J. Moulierac, N. Nisse);
Meeting to prepare a FET2012 "Mobilizing the Cloud: Enabling Multi-User Mobile Outsourcing in the Cloud", Geneva, Switzerland (Januay 12-13, 2012). Attended by J.-C. Bermond and S. Pérennes;
ANR Gratel meeting, Bordeaux, France (November 20, 2012). Attended by J. Araujo (speaker), A. K. Maia and F. Havet (speaker);
Networks Optimization Days, Paris, France (November 30, 2012). Attended by A. Kodjo;
Mascotte project annual seminar, Lac de Sainte-Croix, France (May 10-11, 2012). Attended by most of the Mascotte members;
10th Journées du Pôle ResCom du GDR ASR, Paris, France (November 28-29, 2012). Attended by D. Coudert, A. Kodjo, A. Lancin (speaker), F. Z. Moataz (speaker) and I. Tahiri (speaker);
End of project assessment meeting, Paris, France (July 12, 2012). Attended by S. Pérennes;
TREND Network of Excellence meeting, Volos, Greece (October 1-5, 2012). Attended by L. Chiaraviglio and F. Giroire.
Special event on How Turing's machine changed the world, Lyon, France, July 2-4, 2012. Attended by D. Coudert;
14th Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, La grande Motte, France (May 29th - June 1st, 2012). Attended by C. Caillouet, D. Coudert, A. Lancin, N. Nisse (speaker);
Bordeaux Graph Workshop, Bordeaux, France (November 21-24, 2012). Attended by J. Araujo (speaker), F. Havet (invited speaker), A. K. Maia and R. P. Soares (speaker);
8th ACM International Conference on emerging Networking Experiments and Technologies (ACM CoNEXT) Student Workshop, Nice, France (December 10-13, 2012). Attended by F. Z. Moataz (speaker) and T. K. Phan (speaker);
ECT Workshop spectral properties of complex networks, Trento, Italy (July 23-27, 2012). Attended by J. Galtier and M. Toko Worou (speaker);
Workshop at Fire, Aalborg, Denmark (May 9, 2012). Attended by A. Lancin;
6th International Conference on FUN with Algorithms, Venice, Italy (June 4-6, 2012). Attended by J.-C. Bermond and F. Giroire (speaker);
Workshop Franco-brésilien de Graphes et Optimisation Combinatoire, Plage Redonda, Ceará, Brésil (April 16-20 2012). Attended by J. Araujo, F. Giroire (speaker), F. Havet (speaker), A.K. Maia, N. Nisse, R. Pardo Soares and L. Sampaio Rocha;
5th Workshop on GRAph Searching, Theory and Applications, Banff, Canada (October 8-12, 2012); Attended by N. Nisse (speaker) and R. Pardo Soares;
39th International Colloquium Automata, Languages and Programming, University of Warwick, UK (July 9-12, 2012). Attended by B. Li (speaker);
Journée Thématique "Dynamique des Graphes", Paris, France (July 10th, 2012). Attended by J. Araujo and M. Toko Worou;
14èmes Journées des Graphes et Algorithmes, Clemont-Ferrand, France (November 14-16, 2012). Attended by J. Araujo (speaker), B. Li (speaker), A. K. Maia (speaker), F. Z. Moataz and R. P. Soares (speaker);
Scientific event for celebrating the 20 years of the LIRMM, Montpellier, France, July 12. Attended by D. Coudert;
IFIP TC6 Networking, Prague, Czech Republic (May 21-25, 2012). Attended by T. K. Phan (speaker);
26th ACM/IEEE/SCS Workshop on Principles of Advanced and Distributed Simulation, Zhangjiajie, China (July 15-19, 2012). Attended by A. Lancin (speaker).
11èmes Journées Combinatoire et Algorithmes du Littoral Méditerranéen, Sophia Antipolis, France (February 16th - 17th, 2012). Attended by most of the Mascotte members (speakers: J. Araujo, F. Havet, A. Kodjo, A. Lancin, L. Sampaio);
12èmes Journées Combinatoire et Algorithmes du Littoral Méditerranéen, Montpellier, France (October 11th - 12th, 2012). Attended by J. Araujo and A. K. Maia;
Paris, France (March 28-30 and June 13-14, 2012). Attended by D. Coudert;
L'Ecole de Printemps d'Informatique Théorique, Ile de Ré, France (Mars 26-30, 2012). Attended by A. Lancin, R. Modrzejewski, L. Sampaio and I. Tahiri;
Numerical Analysis Summer School 2012 Stochastic Optimization, Cadarache, France (June 25th- July 6th, 2012). Attended by B. Li.
Summer School on Social Media Modeling and Search, Fira, Santorini, Greece (September 10-14, 2012). Attended by M. Toko Worou;
Licence:
J. Araujo, Algorithmique et Programmation, 30h ETD, Cycle Initial Polytechnique 2, École Polytech’Nice, UNS;
C. Caillouet, Introduction to Operating Systems, 30h ETD, Level L1, IT Tools, 31h, Level L1, Database and advanced information system, 98h, Level L2, IUT Nice Côte d'Azur, UNS;
A. Kodjo, Algorithme-Programmation Objet-Python, 40h ETD, Level L2, UNS;
J. Moulierac and A. Lancin, ASR5 - Networks, 130h ETD, Level L1, IUT Nice Côte d’Azur, UNS;
N. Nisse, informatique, 60h ETD, 1re année classes préparatoires (L1), Lycée International de Valbonne;
M. Syska, Introduction to Operating Systems, 40h ETD, Level L1, Operating Systems : Advanced Programming, 63h ETD, Level L2, Bash Scripting, 15h ETD, Level L3, Introduction to Algorithms, 36h ETD, Level L3, Linux Systems Administration, 24h ETD, Level L3, IUT Nice Côte d’Azur, UNS.
Master:
D. Coudert, Algorithm for Telecom 2, 32h ETD, M2 Ubinet/PENSUNS, UNS;
F. Giroire and N. Nisse, Combinatoire des graphes, 31h ETD, master MDFI, Univ. d'Aix-Marseille, France;
F. Giroire, 16h ETD, Introduction to Probabilities and Statistics, International track of the Master 1 IFI, UNS;
F. Giroire and N. Nisse, Algorithms for Telecommunications, 31h ETD, parcours Ubinet master 2 IFI, UNS.
F. Giroire, F. Havet and N. Nisse, Programmation linéaire et combinatoire, school at ENS Lyon (January 23-27, 2012).
N. Nisse is co-responsible of the Computer Science course of MPSI;
M. Syska is responsible of the Computer Science Department of IUT since september 2011;
J.-C. Bermond is member of the scientific committee;
F. Giroire is responsible of the Internships within international stream Ubinet, Master IFI (http://
J.-C. Bermond is member of the scientific committee of the international track of the M1
(http://
PhD:
J. Araújo, Coloration et convexité dans les graphes, September 13, 2012, J.-C. Bermond, C. Linhares Sales and F. Giroire.
L. Sampaio, Aspects algorithmiques d'heuristiques de coloration de graphes, November 19, 2012, F. Havet.
M. Toko Worou, Outils algorithmiques pour la détection des communautés dans les réseaux, December 7, 2012, J.-C. Bermond and J. Galtier.
PhD in progress:
4th year:
I. Tahiri, Optimisation dans les réseaux de collecte IP sans fils, since November 2009, D. Coudert.
3rd year:
S. Félix, Smart transports : optimisation du trafic dans les villes, since January 2011, J.-C. Bermond and J. Galtier.
A. Lancin, Study of network properties for efficient routing algorithms, since January 2011, D. Coudert.
R. Modrzejewski, Systèmes pair-à-pair de partage de données, since November 2010, S. Pérennes and F. Giroire.
R. Pardo Soares, Routing reconfiguration in WDM networks, since November 2010, D. Coudert and N. Nisse.
2nd year:
T. Al Fares, Trees in digraphs, since September 2011, F. Havet and A. El Sahili (Lebanese University, Beyruth, Lebanon).
M. A. Bergach, GPGPU Graphics Processing Units for signal processing, since September 2011, M. Syska.
A. Kodjo, Design and optimization of multi-operators wireless backhaul networks, since October 2011, D. Coudert.
B. Li, Study of Internet model and its properties for efficient routing algorithms, since October 2011, D. Coudert and N. Nisse.
A. K. Maia, Partitions of directed graphs, since September 2011, F. Havet.
T. K. Phan, Design and Management of networks with low-power Consumption, since October 2011, D. Coudert and J. Moulierac.
1st year:
F. Z. Moataz, Conception et optimisation de réseaux robustes aux pannes et variations de capacités, since October 2012, D. Coudert.
supervised the internship of Guillain Potron (ENS Paris) on sorting algorithms and hull number, June-July 2012 (2 months);
supervised the internship of Fatima Zahra Moataz (M2 Ubinet, Sophia Antipolis) on the diverse routing problem with SRLGs, March-August 2012 (6 months);
supervised the internship of Thomas Bellitto (L3 ENS Cachan - antenne de Bretagne) on linear orderings and graphs decompositions, June-July 2012 (2 months);
supervision of the TIPE of Simon Dorgueil Simon and Yves Barrault on the Analysis of P2P storage system;
supervised the internship of Mélanie Ducoffe (Univ. Nice-Sophia ANtipolis) on cops and robber games in directed graphs, July-August 2012 (2 months).
member of the PhD jury of Julio Araújo (September 13, 2012) and Mikaila Toko Worou (December 7, 2012), University Nice-Sophia Antipolis;
member of the PhD jury of Ahmed Frikha, Université de Rennes (September 28, 2012); member of the PhD jury of Leornardo Sampaio Rocha, University of Nice Sophia Antipolis (November 19, 2012);
external referee of the PhD of Petru Valicov, University of Bordeaux 1 (July 10, 2012); external referee of the PhD of Petr Skoda, Simon Fraser University, Burnaby, BC, Canada (September 13, 2012); external referee of the PhD of Lino Demasi, Simon Fraser University, Burnaby, BC, Canada (October 2, 2012);
Referee and member of the PhD jury of Patricia Maatouk-Kaiser, Supelec Université Libanaise (December 21, 2012).
D. Coudert, F. Giroire and N. Nisse participated to the event at Inria (http://
Several members of Mascotte participated to the documentary "Attention grands travaux : Sophia Antipolis - L'utopie High Tech" for the Public-Sénat channel (watch it online);
J.-C. Bermond is in charge of the attractiveness of the center Inria Sophia Antipolis Méditerannée. He organized Inria days with Athens (February 14-15, and May 21-22, 2012);
F. Giroire presented the stand "Magie et jeux mathématiques" at Sophia Antipolis, France (October 10, 2012);
D. Coudert and C. Castro co-signed an article entitle "Ils débarquent sur votre téléphone : 4G, NFC et Li-Fi ?" on Inriality. Originaly prepared for the series « Le saviez-vous » posted on Inria.fr and twitter;
J.-C. Bermond gave a talk at the evening "Internet et Smartphones" organized at Nice (CUM) on April 10 by SEE Cote d'Azur and la Mairie de Nice Organisation (February 14-15, 2012);
J.-C. Bermond and J.Moulierac wrote an article on Internet and Graph theory for CDC (a journal destined to teachers and students in high schools) ;
F. Havet gave the conference "La hasard fait-il bien les choses ? : une gentille introduction au probabilités" at Rians, France (February 14, 2012);
J.-C. Bermond supervised a brainstorming on scientific mediation with Inria staff members.