Coati is a joint team between Inria Sophia Antipolis - Méditerranée and the I3S laboratory (Informatique Signaux et Systèmes de Sophia Antipolis) which itself belongs to CNRS (Centre National de la Recherche Scientifique) and UNS (Univ. Nice Sophia Antipolis). Its research fields are Algorithmics, Discrete Mathematics, and Combinatorial Optimization, with applications mainly in telecommunication networks.

The main objectives of the Coati project-team are to design networks and communication algorithms. In order to meet these objectives, the team studies various theoretical problems in Discrete Mathematics, Graph Theory, Algorithmics, and Operations Research and develops applied techniques and tools, especially for Combinatorial Optimization and Computer Simulation. In particular, Coati 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.

Coati also investigates other application areas such as bio-informatics, transportation networks and economics.

The research done in Coati results in the production of advanced software such as Grph, and in the contribution to large open source software such as Sagemath.

Members of Coati have a strong expertise in the design and management of wired and wireless backbone, backhaul, broadband, and complex networks. On the one hand, we cope with specific problems such as energy efficiency in backhaul and backbone networks, routing reconfiguration in connection oriented networks (mpls, wdm), traffic aggregation in sonet networks, compact routing in large-scale networks, survivability to single and multiple failures, etc. These specific problems often come from questions of our industrial partners. On the other hand, we study fundamental problems mainly related to routing and reliability that appear in many networks (not restricted to our main fields of applications) and that have been widely studied in the past. However, previous solutions do not take into account the constraints of current networks/traffic such as their huge size and their dynamics. Coati thus puts a significant research effort in the following directions:

**Energy efficiency and Software-Defined Networks (SDN)** at both the design and management levels. More
precisely, we plan to study the deployment of energy-efficient routing algorithm
within SDN. We developed new algorithms in order to take into account
the new constraints of SDN equipments and we evaluate their performance by simulation and by experimentation
on a fat-tree architecture.

**Larger networks:** Another challenge one has to face is the
increase in size of practical instances. It is
already difficult, if not impossible, to solve practical instances optimally
using existing tools. Therefore, we have to find new ways to solve
problems using reduction and decomposition methods, characterization of
polynomial instances (which are surprisingly often the practical ones), or
algorithms with acceptable practical performances.

**Stochastic behaviors:** Larger topologies mean frequent changes due
to traffic and radio fluctuations, failures, maintenance
operations, growth, routing policy changes, etc. We aim at including these
stochastic behaviors in our combinatorial optimization process to handle the
dynamics of the system and to obtain robust designs of networks.

Coati is mostly interested in telecommunications networks. Within this domain, we consider applications that follow the needs and interests of our industrial partners, in particular Orange Labs or Nokia Bell-Labs, but also SME like 3-Roam.

We focus on the design and management of heterogeneous networks. The project has kept working on the design of backbone networks (optical networks, radio networks, IP networks). We also study routing algorithms such as dynamic and compact routing schemes, as we did in the context of the FP7 EULER led by Alcatel-Lucent Bell-Labs (Belgium), and the evolution of the routing in case of any kind of topological modifications (maintenance operations, failures, capacity variations, etc.).

Our combinatorial tools may be well applied to solve many other problems in various areas (transport, biology, resource allocation, chemistry, smart-grids, speleology, etc.) and we intend to collaborate with experts of these other domains.

For instance, we have recently started a collaboration in Structural Biology with EPI ABS (Algorithms Biology Structure) from Sophia Antipolis (described in Section ). Furthermore, we are working on robot moving problems coming from Artificial Intelligence/Robotic in collaboration with Japan Advanced Institute of Science and Technology. In the area of transportation networks, we have started a collaboration with Amadeus on complex trip planning, and a collaboration with SME Instant-System on dynamic car-pooling combined with multi-modal transportation systems. Last, we have started a collaboration with GREDEG (Groupe de Recherche en Droit, Economie et Gestion, Univ. Nice Sophia Antipolis) on the analysis and the modeling of systemic risks in networks of financial institutions.

David Coudert and Nathann Cohen (LRI) won the Flinders Hamiltonian Cycle Problem (FHCP) Challenge 2016 (http://

Fatima Zahra Moataz, former PhD student of Coati, is the recipient of an accessit to the PhD prize Graphes “Charles Delorme” 2016 for her PhD thesis entitled “Towards Efficient and Fault-Tolerant Optical Networks: Complexity and Algorithms”.

Functional Description

The objective of BigGraphs is to provide a distributed platform for very large graphs processing. A typical data set for testing purpose is a sample of the Twitter graph : 240GB on disk, 398M vertices, 23G edges, average degree of 58 and max degree of 24635412.

We started the project in 2014 with the evaluation of existing middlewares (GraphX / Spark and Giraph / Hadoop). After having tested some useful algorithms (written according to the BSP model) we decided to develop our own platform.

This platform is based on the existing BigGrph library and we are now in the phasis where we focus on the quality and the improvement of the code. In particular we have designed strong test suites and some non trivial bugs have been fixed. We also have solved problems of scalability, in particular concerning the communication layer with billions of messages exchanged between BSP steps. We also have implemented specific data structures for BSP and support for distributed debugging. This comes along with the implementation of algorithms such as BFS or strongly connected components that are run on the NEF cluster.

Participants: Luc Hogie, Nicolas Chleq, David Coudert, Michel Syska.

Partner: This project is a joint work of the three EPI Coati, Diana and Scale and is supported by an ADT grant.

Contact: Luc Hogie

Additional softwares

The following software are useful tools that bring basic services to the platform (they are not dedicated to BigGrph). Participants : Luc Hogie, Nicolas Chleq

Jac-a-boo is a framework aiming at facilitating the deployment and the bootstrapping of distributed Java applications over Share-Nothing Clusters (SNCs). The primary motivation for developing Jac-a-boo is to have an efficient and comprehensive deployment infrastructure for the BigGrph distributed graph library. http://

ldjo (Live Distributed Java Objects) is a framework for the development and the deployment of Java distributed data structures. Alongside with data aspect of distributed data structures, ldjo comes with mechanisms for processing them in a distributed/parallel way. In particular it provides implementations of Map/Reduce and Bulk Synchronous Parallel (BSP). http://

Octojus provides an object-oriented RPC (Remote Procedure Call) implementation in Java. At a higher abstraction level, Octojus provides a framework for the development of systolic algorithms, a batch scheduler, as well as an implementation of Map/Reduce. The latter is used in the BigGrph graph computing platform. http://

The high performance graph library for Java

Functional Description

Grph is an open-source Java library for the manipulation of graphs. Its main design objectives are to make it simple to use and extend, efficient, and, according to its initial motivation: useful in the context of graph experimentation and network simulation. Grph also has the particularity to come with tools like an evolutionary computation engine, a bridge to linear solvers, a framework for distributed computing, etc.

Grph achieves great efficiency through the use of multiple code optimization techniques such as multi-core parallelism, caching, performant data structures and use of primitive objects, interface to CPLEX linear solver, exploitation of low-level processor caches, on-the-fly compilation of specific C/C++ code, etc.

Unlike other graph libraries which impose the user to first decide if he wants to deal with directed, undirected, hyper (or not) graph, the model offered by Grph is unified in a very general class that supports mixed graphs made of undirected and directed simple or hyper edges.

We have identified more than 600 users of Grph since 2013. Inside Inria we collaborate with the Aoste EPI, for example we recently added a new algorithm (proposed by N. Cohen / LRI) for iterating over the cycles of a given graph in the TimeSquare tool. We also have integrated the discrete-events simulation engine of DRMSim and some dynamic models (evolution of the connectivity with the mobility of nodes) to Grph. Grph includes bridges to other graph libraries such as JUNG, JGraphT, CORESE (a software developed by the WIMMICS team Inria-I3S), LAD (C. Solnon, LIRIS), Nauty (B. D. McKay) or Sagemath. L. Viennot has proposed an implementation of the 4-sweep diameter algorithm designed at LIAFA .

Participants: Luc Hogie, Nathann Cohen, David Coudert and Michel Syska.

Contact: Luc Hogie

SageMath

SageMath is a free open-source mathematics software system, initially created by William Stein (Professor of mathematics at Washington University), and now maintained by a large community of contributors. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers.

We contribute the addition of new graph algorithms along with their documentations and the improvement of underlying data structures.

Contact: David Coudert

Network design is a very wide subject which concerns all kinds of networks. In telecommunications, networks can be either physical (backbone, access, wireless, ...) or virtual (logical). 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) paths between their end nodes. The set of paths is chosen according to the technology, the protocol or the QoS constraints.

We mainly focus on three topics: firstly Fixed wireless Backhaul Networks, with the objective of achieving a high reliability of the network. Secondly, Software-Defined networks, in which a centralized controller is in charge of the control plane and takes the routing decisions for the switches and routers based on the network conditions. This new technology brings new constraints and therefore new algorithmic problems such as the problem of limited space in the switches to store the forwarding rules. Finally, the third topic investigated is Energy Efficiency within Backbone networks and for content distribution. We focus on Redudancy Elimination, and we use SDN as a tool to turn-off the links in real networks. We validated our algorithms on a real SDN platform

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 context, the optimization criterion for these objects is no longer the number of edges they use, but the number of SRLGs involved. Unfortunately, computing these combinatorial objects is NP-hard and hard to approximate with this objective in general. Nevertheless some objects can be computed in polynomial time when the SRLGs satisfy certain structural properties of locality which correspond to practical ones, namely the star property (all links affected by a given SRLG are incident to a unique node) and the span 1 property (the links affected by a given SRLG form a connected component of the network). The star property is defined in a multi-colored model where a link can be affected by several SRLGs while the span property is defined only in a mono-colored model where a link can be affected by at most one SRLG. We have extended in these notions to characterize new cases in which these optimization problems can be solved in polynomial time. We have also investigated the computational impact of the transformation from the multi-colored model to the mono-colored one. Reported experimental results validate the proposed algorithms and principles.

The reliability of a fixed wireless backhaul network is the probability that the network can meet all the communication requirements considering the uncertainty (e.g., due to weather) in the maximum capacity of each link. In , we provide an algorithm to compute the exact reliability of a backhaul network, given a discrete probability distribution on the possible capacities available at each link. The algorithm computes a conditional probability tree, where each leaf in the tree requires a valid routing for the network. Any such tree provides an upper and lower bound on the reliability, and the algorithm improves these bounds by branching in the tree. We also consider the problem of determining the topology and configuration of a backhaul network that maximizes reliability subject to a limited budget. We provide an algorithm that exploits properties of the conditional probability tree used to calculate reliability of a given network design. We perform a computational study demonstrating that the proposed methods can calculate reliability of large backhaul networks, and can optimize topology for modest size networks.

Software-defined Networks (SDN), in particular OpenFlow, is a new networking paradigm enabling innovation through network programmability. SDN is gaining momentum with the support of major manufacturers. Over past few years, many applications have been built using SDN such as server load balancing, virtual-machine migration, traffic engineering and access control.

While SDN brings flexibility in the management of flows within the data center fabric, this flexibility comes at the cost of smaller routing table capacities. Indeed, the Ternary Content Addressable Memory (TCAM) needed by SDN devices has smaller capacities than CAMs used in legacy hardware. In , , we investigate compression techniques to maximize the utility of SDN switches forwarding tables. We validate our algorithm, called Minnie, with intensive simulations for well-known data center topologies, to study its efficiency and compression ratio for a large number of forwarding rules. Our results indicate that Minnie scales well, being able to deal with around a million of different flows with less than 1000 forwarding entry per SDN switch, requiring negligible computation time. To assess the operational viability of MINNIE in real networks, we deployed a testbed able to emulate a

Due to the increasing impact of ICT (Information and Communication Technology) on power consumption and worldwide gas emissions, energy efficient ways to design and operate backbone networks are becoming a new concern for network operators. Recently, energy-aware routing (EAR) has gained an increasing popularity in the networking research community. The idea is that traffic demands are redirected over a subset of the network devices, allowing other devices to sleep to save energy. We studied variant of this problems.

To optimize energy efficiency in network, operators try to switch off as many network devices as possible. 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. We formulate this problem as Energy Efficient Content Distribution. The objective is to find a feasible routing, so that the total energy consumption of the network is minimized subject to satisfying all the demands and link capacity. We exhibit the range of parameters (size of caches, popularity of content, demand intensity, etc.) for which caches are useful. Experiment results show that by placing a cache on each backbone router to store the most popular content, along with well choosing the best content provider server for each demand to a CDN, we can save a total up to 23% of power in the backbone, while 16% can be gained solely thanks to caches.

Network Function Virtualization (NFV) is a promising network architecture concept to reduce operational costs. In legacy networks, network functions, such as firewall or TCP optimization, are performed by specific hardware. In networks enabling NFV coupled with the Software Defined Network (SDN) paradigm, network functions can be implemented dynamically on generic hardware. This is of primary interest to implement energy efficient solutions, which imply to adapt dynamically the resource usage to the demands. In , , we study how to use NFV coupled with SDN to improve the energy efficiency of networks. We consider a setting in which a flow has to go through a Service Function Chain, that is several network functions in a specific order. We propose a decomposition model that relies on lightpath configuration to solve the problem. We show that virtualization allows to obtain between 30% to 55% of energy savings for networks of different sizes.

Coati 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 use graph theory to model various network problems. 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 from
which the problems are polynomial-time solvable. Many results introduced here are presented in detail in the PhD thesis of Guillaume Ducoffe on *Metric properties of large graphs* https://

It is well known that many NP-hard problems are tractable in the class of bounded treewidth graphs. In particular, tree-decompositions of graphs are an important ingredient of dynamic programming algorithms for solving such problems. This also holds for other width-parameters of graphs. Therefore, computing these widths and associated decompositions of graphs has both a theoretical and practical interest.

Many tree-decomposition-like parameters are related to particular layouts (ordering) of the vertices of the input graph. In , we present a new set of constraints for modeling linear ordering problems on graphs using Integer Linear Programming (ILP). These constraints express the membership of a vertex to a prefix rather than the exact position of a vertex in the ordering. We use these constraints to propose new ILP formulations for well-known linear ordering optimization problems, namely the Pathwidth, Cutwidth, Bandwidth, SumCut and Optimal Linear Arrangement problems. Our formulations are not only more compact than previous proposals, but also more efficient as shown by our experimental evaluations on large benchmark instances.

The decomposition of graphs by clique-minimal separators is a common algorithmic tool, first introduced by Tarjan. Since it allows to cut a graph into smaller pieces, it can be applied to pre-process the graphs in the computation of many optimization problems. However, the best known clique-decomposition algorithms have respective

In , , we study metric properties of the bags of tree-decompositions of graphs. Roughly, the length and the breadth of a tree-decomposition are the maximum diameter and radius of its bags respectively. The treelength and the treebreadth of a graph are the minimum length and breadth of its tree-decompositions respectively. Pathlength and pathbreadth are defined similarly for path-decompositions. In this paper, we answer open questions of [Dragan and Köhler , Algorithmica 2014] and [Dragan, Köhler and Leitert, SWAT 2014] about the computational complexity of treebreadth, pathbreadth and pathlength. Namely, we prove that computing these graph invariants is NP-hard. We further investigate graphs with treebreadth one, i.e., graphs that admit a tree-decomposition where each bag has a dominating vertex. We show that it is NP-complete to decide whether a graph belongs to this class. We then prove some structural properties of such graphs which allows us to design polynomial-time algorithms to decide whether a bipartite graph, resp., a planar graph, has treebreadth one.

The Gromov hyperbolicity is an important parameter for analyzing complex networks which expresses how the metric structure of a network looks like a tree (the smaller gap the better). It has recently been used to provide bounds on the expected stretch of greedy-routing algorithms in Internet-like graphs, and for various applications in network security, computational biology, the analysis of graph algorithms, and the classification of complex networks.

Topologies for data center networks have been proposed in the literature through various graph classes and operations. A common trait to most existing designs is that they enhance the symmetric properties of the underlying graphs. Indeed, symmetry is a desirable property for interconnection networks because it minimizes congestion problems and it allows each entity to run the same routing protocol. However, despite sharing similarities these topologies all come with their own routing protocol. Recently, generic routing schemes have been introduced which can be implemented for any interconnection networks. The performances of such universal routing schemes are intimately related to the hyperbolicity of the topology. Motivated by the good performances in practice of these new routing schemes, we propose in , the first general study of the hyperbolicity of data center interconnection networks. Our findings are disappointingly negative: we prove that the hyperbolicity of most data center topologies scales linearly with their diameter, that it the worst-case possible for hyperbolicity. To obtain these results, we introduce original connection between hyperbolicity and the properties of the endomorphism monoid of a graph. In particular, our results extend to all vertex and edge-transitive graphs. Additional results are obtained for de Bruijn and Kautz graphs, grid-like graphs and networks from the so-called Cayley model.

We study several two-player games on graphs.

Graph Searching is a game where a team of searchers aims at capturing a fugitive in a graph. Graph Searching games have been widely studied because they are an algorithmic interpretation of tree/path-decompositions of graphs.

In , we define a new variant of graph searching, where searchers have to capture an invisible fugitive with the constraint that no two searchers can occupy the same node simultaneously. This variant seems promising for designing approximation algorithms for computing the pathwidth of graphs. The main contribution in is the characterization of trees where k searchers are necessary and sufficient to win. Our characterization leads to a polynomial-time algorithm to compute the minimum number of searchers needed in trees.

We also study graph searching in directed graphs. We prove that the graph processing variant is monotone which allows us to show its equivalence with a particular digraph decomposition .

We also investigate the games described above in a distributed setting.

Consider a set of mobile robots with minimal capabilities placed over distinct nodes of a discrete anonymous ring. Asynchronously, each robot takes a snapshot of the ring, determining which nodes are either occupied by robots or empty. Based on the observed configuration, it decides whether to move to one of its adjacent nodes or not. In the first case, it performs the computed move, eventually. The computation also depends on the required task. In , we solve both the well-known Gathering and Exclusive Searching tasks. In the former problem, all robots must simultaneously occupy the same node, eventually. In the latter problem, the aim is to clear all edges of the graph. An edge is cleared if it is traversed by a robot or if both its endpoints are occupied. We consider the exclusive searching where it must be ensured that two robots never occupy the same node. Moreover, since the robots are oblivious, the clearing is perpetual, i.e., the ring is cleared infinitely often. In the literature, most contributions are restricted to a subset of initial configurations. Here, we design two different algorithms and provide a characterization of the initial configurations that permit the resolution of the problems under minimal assumptions.

We also investigate several graph problems coming from various applications. We mainly consider their complexity in general or particular graph classes. When possible, we present polynomial-time (approximation) algorithms or Fixed Parameter Tractable algorithms.

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 . Given a set V of items with positive integer weights, an underlying graph G = (V, E), and an integer q, the goal is to pack the items into a minimum number of bins so that (i) the total weight of the items packed in every bin is at most q, and (ii) for each edge (i, j) ∈ E there is at least one bin containing both items i and j. We first show that when the underlying graph is unweighted (i.e., all the items have equal weights), the problem is equivalent to the q-clique problem, and when furthermore the underlying graph is a clique, optimal solutions are obtained from covering designs. We prove that the problem becomes NP-hard even for weighted paths and un-weighted trees and we propose approximation algorithms for particular families of graphs, including: a

For every connected graph

Many notions in graph convexity have been defined and studied for various applications, such as geode-tic convexity (generalizing the classical convexity in Euclidean space to graphs), monophonic convexity (to model spreading of rumor or disease in a network), etc. Each of the convexity notions led to the study of important graph invariants such as the hull number (minimum number of vertices whose hull set is the entire graph) or the interval number (minimum number of vertices whose interval is the whole graph). Recently, Araujo et al. introduced the notion of Cycle Convexity of graphs for its application in Knot Theory. Roughly, the tunnel number of a knot embedded in a plane is equivalent to the hull number of a corresponding planar 4-regular graph in cycle convexity. In , we study the interval number of a graph in cycle convexity. Precisely, given a graph G, its interval number in cycle convexity, denoted by incc(G), is the minimum cardinality of a set

Coati also studies theoretical problems in graph theory. If some of them are directly motivated by applications (see Subsection ), others are more fundamental. In particular, we are putting an effort on understanding better directed graphs (also called *digraphs*) and partionning problems, and in particular colouring problems. We also try to better the understand the many relations between orientation and colourings.
We study various substructures and partitions in (di)graphs. For each of them, we aim at giving sufficient conditions that guarantee its existence and at determining the complexity of finding it.

The concept of arc-disjoint flows in networks was introduced by Bang-Jensen and Bessy [Theoret. Comput. Science 526, 2014]. This is a very general framework within which many well-known and important problems can be formulated. In particular, the existence of arc-disjoint branching flows, that is, flows which send one unit of flow from a given source

an NP-complete problem to decide whether a network

a polynomial problem to decide whether a network

The algorithm for the later result generalizes the polynomial-time algorithm, due to Lovász, for deciding whether a given input digraph has two arc-disjoint out-branchings rooted at a given vertex.
Finally we prove that under the so-called Exponential Time Hypothesis (ETH), for every

An *oriented cycle* is an orientation of a undirected cycle. In , , we first show that for any oriented cycle

A * $k$-partition* of a (di)graph

A famous conjecture of Gyárfás and Sumner states for any tree

A graph *locally irregular* if every two adjacent vertices of *locally irregular decomposition* of

An orientation of a graph *proper* if two adjacent vertices have different indegrees. The *proper-orientation number* of a graph

A * $k$-edge-weighting* of a graph

One of the variants consists in considering total-labelling rather than edge-weighting.
A * $k$-total-weighting* of a graph

We wish to motivate the problem of finding decentralized lower-bounds on the complexity of computing a Nash equilibrium in graph games. While the centralized computation of an equilibrium in polynomial time is generally perceived as a positive result, this does not reflect well the reality of some applications where the game serves to implement distributed resource allocation algorithms, or to model the social choices of users with limited memory and computing power. As a case study, we investigate in on the parallel complexity of a game-theoretic variation of graph colouring. These “colouring games" were shown to capture key properties of the more general welfare games and Hedonic games. On the positive side, it can be computed a Nash equilibrium in polynomial-time for any such game with a local search algorithm. However, the algorithm is time-consuming and it requires polynomial space. The latter questions the use of colouring games in the modeling of information-propagation in social networks. We prove that the problem of computing a Nash equi- librium in a given colouring game is PTIME-hard, and so, it is unlikely that one can be computed with an efficient distributed algorithm. The latter brings more insights on the complexity of these games.

Let *neighborhood* of a vertex *closed neighborhood* is the set *identifying code* in

Particular interest was dedicated to grids as many processor networks have a grid topology. There are three types of regular infinite grids in the plane, namely the hexagonal grids, the square grids and the triangular grids.
In , , we study the square grid

The Instant System startup company develop a platform in the area of Intelligent transportation systems (ITS). The partnership with Coati aims at designing algorithms for itinerary planning in multimodal transportation networks. The main objective is to combine public transport system and dynamic car-pooling.

The STINT project (*STructures INTerdites*) is led by the MC2 group (LIP, ENS-Lyon) and involves the G-SCOP laboratory (Grenoble).

The aim of STINT is to answer the following fundamental question: *given a (possibly infinite) family $\psi $ of graphs, what properties does a $\psi $-free graph have?* To this end, it will firstly establish bounds on some classical graph parameters (e.g., clique number, stability number, chromatic number) for

The SYSTEMIC project was led by COATI and involves the LAMA (Paris Est), GREDEG (Sophia Antipolis) and CREM (Rennes) laboratories.

The aim of SYSTEMIC was to bring together the expertises of researchers in economics, graph theory and financial mathematics to propose new models to evaluate the systemic risk of networks of financial institutions, and to propose new methods to mitigate the risk of contagions in such networks. The novelty of the project was in particular to consider strategies for a dynamic control of heterogeneous networks.

Réseaux de communications, working group of GDR RSD, CNRS.

Action Graphes, working group of GDR IM, CNRS.

AOR (Vassilis Zissimopoulos) : University of Athens, Department of Informatics and Telecommunications (Greece)

Combinatorial Optimization, Games and Applications (COGA), June 2015- September 2016

Participants : Jean-Claude Bermond, David Coudert, Frédéric Giroire, Nicolas Nisse, Stéphane Pérennes

**Inria Chile**

Associate Team involved in the International Lab:

Title: distributed ALgorithms for DYnamic NETworks

International Partner (Institution - Laboratory - Researcher):

Universidad Adolfo Ibañez (Chile) - Facultad de Ingeniería y Ciencias - Karol SUCHAN

Start year: 2016

This associated team would be the natural continuation of the fruitful EA AlDyNet (2013-2015, https://team.inria.fr/coati/projects/aldynet/)

The main goal of this Associate Team is to design and implement practical algorithms for computing graph structural properties. We will then use these algorithms on a concrete case of study which concerns the transportation network of the Santiago agglomeration. We are both interested in theoretical results concerning the feasibility of computing graph properties, and by their practical implementation (using SageMath, www.sagemath.org/) for our application and their diffusion in the scientific community. There are three main objectives:

1) Design efficient algorithms to compute important graph properties (hyperbolicity, treelength, centrality, treewidth...) in real networks. We are not only interested by the worst-case time-complexity of these algorithms but by their performance in practice.

2) Implement and document our algorithms using the open-source framework SageMath. One advantage of using SageMath is that it has interfaces with other graph libraries (igraph, Boost...) and with Linear Programming solver (GLPK, Cplex...). Moreover, the success of SageMath (which has accumulated thousands of users over the last 10 years) will participate to the diffusion of our algorithms.

3) Apply our algorithms on the Santiago transportation network that have been collected by our Chilean partner during the last year of AlDyNet (2013-2015). Based on the results, propose tools for decision support in designing bus routes, timetables, etc. More precisely, we have collected information about the use of public transport (data of smart cards for automatic fare collection -BIP-, bus routes and bus schedules, etc.), urban infrastructure information, schools’ addresses, and approximate locations where students live. We have started to clean and consolidate these data. We will then develop decision support tools, for example, for improving quality education accessibility.

Apart from formal collaboration Coati members maintain strong connections with the following international teams, with regular visits of both sides.

Univ. of Southern Denmark, Prof. Jorgen Bang Jensen

RWTH Aachen Univ., Lehrstuhl II für Mathematik, Germany, Prof. Arie M.C.A. Koster

Concordia Univ. - Montréal, Quebec, Canada, Prof. Brigitte Jaumard

GAIATO : Graphs and Algorithms Applied to Telecommunications, International Cooperation FUNCAP/FAPs/Inria/INS2i-CNRS, no. INC-0083-00047.01.00/13, with Federal University of Ceará, Brasil, 2014-2016.

Daniela Aguirre Guerrero

Universitat de Girona, Girona, Spain, Visiting PhD Student, from Sep 2016 until Nov 2016.

Jean Francois Baffier

Japanese-French Laboratory for Informatics UMI 3527, Japan, Visiting Scientist, June 2016.

Jorgen Bang Jensen

University of Southern Denmark, Odensee, Denmark, Visiting Scientist, from June 2016 until Jul 2016.

Augustin Chaintreau

Columbia University, New York, US, Visiting Scientist, 19-21st January 2016.

Clément Charpentier

Université Joseph Fourier, Grenoble, France, Visiting Scientist, 21-26th February 2016.

Romuald Elie

Université Paris-Est Marne-la-Vallée, Visiting Scientist, October 24-November 2, 2016.

Takako Kodate

Tokyo Woman's Christian Univ., Japan, Visiting Scientist, Apr 2016.

Christian Konrad

Reykjavik University, Iceland, Visiting Scientist, February 28th to March 3rd, 2016.

Aurélie Lagoutte

Université de Princeton, USA, 9-11th March, 2016.

Zvi Lotker

Ben Gurion University of the Negev, Israel, 22-27th February, 2016.

Ana Karolinna Maia De Oliveira

Univ. Federal do Ceara, Fortaleza, Brazil, Visiting Scientist, Oct 2016.

Colin McDiarmid

University of Oxford, UK, Visiting Scientist, September 26-30th 2016.

Ioannis Milis

Athens University of Economics and Business, Athens, Greece, Visiting Scientist, Feb 2016.

Eduardo Moreno

Univ. Adolfo Ibanez, Santiago, Chile, Visiting Scientist, Sep 2016.

Julio Cesar Silva Araujo

Univ. Federal do Ceara, Fortaleza, Brazil, Visiting Scientist, Oct 2016.

Guillem Perarnau-Llobet

University of Birmingham, UK, Visiting Scientist, May 9-13rd 2016.

Jean-Sébastien Sereni

CNRS, France, 22-25th February.

Yllka Velaj

Gran Sasso Science Institute, L'Aquila, Italia, Visiting PhD Student, from Feb 2016 until Apr 2016.

Joseph Yu

University of the Fraser Valley, Abbotsford, Canada, Visiting Scientist, Apr 2016.

Vassilis Zissimopoulos

National and Kapodistrian University of Athens, Athens, Greece, Visiting Scientist, Feb 2016.

Julien Bensmail

LaBRI, University of Bordeaux, October 10-14, 2016;

LIF, Aix-Marseille University, October 17-19, 2016.

Jean-Claude Bermond

Department of Informatics and Telecommunications of the National and Kapodistrian University of Athens, Greece, June7-21, 2016.

David Coudert

LIP6, UPMC, Paris, October 11-13, 2016;

Univ. Adolfo Ibañez and Univ. Chile, Santiago, Chile, in the context of Inria associated team AlDyNet, October 24-November 11, 2016.

Frédéric Giroire

Orange Labs, Chatillon, May 17-20, 2016;

Computer Science and Software Engineering department, Concordia University, Montréal, Canada, September 28-October 7, 2016.

Nicolas Huin

Concordia University, Montreal, Canada, August 22-November 22, 2016.

William Lochet

Université libre de Bruxelles, Belgique, June 20-25th, 2016.

Nicolas Nisse

Univ. Federal do Ceará, Fortaleza, Brazil, April, 2016;

LIF, Aix-Marseille University, July 18-22, 2016;

Univ. Adolfo Ibañez and Univ. Chile, Santiago, Chile, in the context of Inria associated team AlDyNet, October 24-November 11, 2016.

Bruce Reed

National Institute of Informatics Tokyo Japan, June 1-28th 2016;

Pacific Institute of Mathematical Sciences, June 28th-September 5th 2016;

National Institute of Informatics Tokyo Japan, October 1st-December 31th 2016.

Frédéric Havet

GCO 2016: 2nd French Brazilian Workshop on Graphs and Combinatorial Optimization, Redonda, Ceara, Brazil, May 28-April 1, 2016;

4th STINT meeting, January 25-27, Saint Bonnet de Champsaur, France;

Workshop on Shannon capacity, September 11-16, Cassis, France.

Bruce Reed

Workshop on Shannon capacity, September 11-16, Cassis, France.

David Coudert

ONDM'16 : 20th International Conference on Optical Networking Design and Modeling, Cartagena, Spain, May 9-12, 2016;

IEEE ICC'16 : IEEE International Conference on Communications, Kuala Lumpur, Malaysia, May 23-27, 2016;

USRR'16 : 4th International Workshop on Understanding the Inter-play between Sustainability, Resilience and Robustness in networks, Halmstad, Sweden, September 15, 2016;

IEEE Globecom'16 : IEEE Global Communications Conference, Washington, DC, USA, December 4-8, 2016.

Frédéric Havet

AAIM 2016: 11th International Conference on Algorithmic Aspects in Information and Management, Bergamo, Italy, July 18-20, 2016;

JGA 2016: 18th Journées Graphes et Algorithmes, Paris, France, November 16-18, 2016.

Nicolas Nisse

AlgoTel 2016: 18es Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Bayonne, France, 24-27 May, 2016.

Jean-Claude Bermond

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 the SIAM book series on Discrete Mathematics, Transactions on Network Optimization and Control , Discrete Mathematics, Algorithms and Applications.

David Coudert

Discrete Applied Mathematics (Elsevier); Networks (Wiley).

Frédéric Havet

Discrete Mathematics and Theoretical Computer Science;

Nicolas Nisse

Guest editor of Special issue on Theory and Applications of Graph Searching Problems for Theoretical Computer Science (December 2016).

Bruce Reed

Journal of Graph Theory, Electronic Journal of Combinatorics;

Members of COATI have reviewed numerous manuscripts submitted to international journals, including: Algorithmica, Algorithms, Bulletin of the Malaysian Mathematical Sciences Society, Computer Communications, Computer Networks, Computers & Operations Research, Discrete Applied Mathematics, European Journal of Operational Research, IEEE/OSA Journal of Lightwave Technology, Networks, Photonic Network Communications, The Computer Journal, Theoretical Computer Science, IEEE/ACM Transactions on Communications, IEEE/ACM Transactions on Networking, IEEE Transactions on Network and Service Management, etc.

David Coudert

*On the design of reliable wireless backhaul networks*. International Conference on Ad Hoc Networks and Wireless (AdHoc-Now’16), Lille, France (July 4-5, 2016);

*On the notion of hyperbolicity in graphs*. Seminar of the Complex Networks team, LIP6, UPMC, Paris (October 12, 2016).

Nicolas Nisse

*Spy Games*. Groupe de travail de l'équipe CRO, LIF, Marseille, July 18th, 2016;

*Recovery of disrupted airline operations*. Seminar of LIMOS, Univ. Blaise Pascal, Clermont-Ferrand, January 28th, 2016.

Bruce Reed

The Typical Structure of H-Free Graphs. Sao Paulo Advanced School on Algorithms, Combinatorics, and Optimization, Sao Paulo, Brazil, July 216;

How To Determine If A Random Graph With A Fixed Degree Sequence Has A Giant Component. Sao Paulo Advanced School on Algorithms, Combinatorics, and Optimization, Sao Paulo, Brazil. July 2016;

On The Structure Of Typical H-Free Graphs. University of Birmingham Combinatorics Seminar, Birmingham, United Kingdom, May 2016;

How To Determine If A Random Graph With A Fixed Degree Sequence Has A Giant Component. Simon Fraser University, July 2016;

40th Australian Conference on Combinatorial Mathematics and Combinatorial Computing, NewCastle Australia, December 2016;

How To Determine If A Random Graph With A Fixed Degree Sequence Has A Giant Component. 13th Workshop on Algorithms and Models for the Wb Graph, Montreal, Canada, December 2016.

David Coudert

Member of the steering committee of *Pôle ResCom du GDR RSD du CNRS* (since 2005);

Member of the steering committee of *Rencontres francophones sur les aspects algorithmiques des télécommunications* (AlgoTel).

Frédéric Havet

Member of the steering committee of *GT Graphes du GDR IM du CNRS*;

Member of the steering committee of *Journées Graphes et Algorithmes (JGA)*;

Member of the steering committee of *Journée Combinatoire et Algorithmes du Littoral Méditerranéen (JCALM)*.

Bruce Reed

Member of the selection committee for the CRM-Fields-Pims Prize.

Jean-Claude Bermond

Expert for DRTT-MESR (Crédit impôt recherche(CIR et agréments) and various projects outside France.

David Coudert

Expert for the Future and Emerging Technologies Open Scheme (FET-Open) European program, and the ANR.

Frédéric Giroire

Expert for ANR.

Frédéric Havet

Expert for ANR.

Michel Syska

Expert for DRTT PACA.

Jean-Claude Bermond

Responsible fo the cooperation between Inria and Greece (meeting with the french Embassy in greece, obtention of join grants and of financial support for internships via the Bodossakis Fundation).

David Coudert

Scientific coordinator of the evaluation seminar of the Inria theme “Networks and Telecommunications”, Rungis, France, March 22-24, 2016.

Frédéric Havet

Responsible of the ComRed Team of I3S;

Recruiting committee (comité de sélection) University of Nice Sophia Antipolis.

Michel Syska

Elected member of CPRH (Comité Permanent de Ressources Humaines) University of Nice Sophia Antipolis;

Recruiting committee (comité de sélection) University of Nice Sophia Antipolis.

**Licence**

Pierre Aboulker

*Recherche opérationnelle*, 74h ETD, Niveau L2, IUT de Nice Côte d'Azur, UNS.

Julien Bensmail

*Système d'information et logistique*, 36h ETD, niveau S3, IUT Nice Côte d’Azur, UNS.

Christelle Caillouet

*Database and advanced information system*, 36h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Delivery Optimization*, 30h ETD, Level L3, IUT Nice Côte d’Azur, UNS;

*Introduction to Programming*, 60h ETD, Level L1, IUT Nice Côte d’Azur, UNS;

Guillaume Ducoffe

*Introduction au Web*, 28h30 ETD, Level L2, Polytech Nice Sophia, France

*Programmation Orientée Objet*, 39h ETD, Level L2, Polytech Nice Sophia, France

*Principes des systèmes d'exploitation*, 26h ETD, Level L2, IUT de Nice Côte d'Azur, UNS.

Valentin Garnero

*Introduction aux systèmes informatiques*, 108h, niveau S1, IUT Nice Côte d’Azur, UNS.

Luc Hogie

*Programmation Répartie*, 36h ETD, IUT Nice Côte d’Azur, UNS.

Nicolas Huin

*Introduction aux réseaux*, 21h ETD, niveau S1, IUT Nice Côte d’Azur, UNS.

William Lochet

*Paradigmes et interprétation*, 18h ETD, L3, Univ. Côte d'Azur

*Programmation objet*, 18h ETD, L3, Univ. Côte d'Azur

*Compilation*, 18h ETD, L3, Univ. Côte d'Azur

*Projet scientifique*, 30h ETD, L2, Univ. Côte d'Azur

*Informatique générale*, 36h ETD, L1, Univ. Côte d'Azur

*Intro programmation C*, 12h ETD, L1, Univ. Côte d'Azur

Joanna Moulierac

*Networks*, 100h ETD, L1, IUT Nice Côte d’Azur, UNS.

Nicolas Nisse

*Introduction à l'algorithmique*, 24h ETD, MPSI, Lycée International Valbonne, France.

Steven Roumajon

*Architecture des réseaux*, 48h ETD, L2, IUT Nice Côte d’Azur, UNS.

Michel Syska

*Operating Systems: Advanced Programming*, 40h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Data Structures and Algorithms*, 20h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Algorithmics*, 30h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Distributed Programming*, 30h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Bash Scripting*, 30h ETD, Level L3, IUT Nice Côte d’Azur, UNS;

*Introduction to Algorithms and Complexity*, 60h ETD, Level L3, IUT Nice Côte d’Azur, UNS;

*Linux System Administration*, 35h ETD, Level L3, IUT Nice Côte d’Azur, UNS.

**Master**

David Coudert

*Algorithms for Telecoms*, 32h ETD, stream UbiNet of Master 2 IFI and Master RIF, UNS.

Frédéric Giroire,

*Algorithmics of Telecommunications*, 18h ETD, stream UbiNet of Master 2 IFI, UNS;

*Green Networks*, 18h ETD, stream UbiNet of Master 2 IFI, UNS;

*Introduction to probability and statistics*, 15h ETD, International Master 1, UNS;

Frédéric Havet

*Graph colouring*, 4h ETD, M2 MDFI, Aix Marseille Univ., France.

Nicolas Nisse

*Graph Algorithms*, 18h ETD, M2 IFI, parcours UBINET, UNS, France.

*Resolution Methods*, 15h ETD, M1 international, UNS, France;

*Graph decompositions*, 4h ETD, M2 MDFI, Aix Marseille Univ. , France

Stéphane Pérennes

*Calcul concurrent et distribué en Java*, 30h TP, Master 1 Miage. Polytec Nice.

**Responsabilités pédagogiques**

Julien Bensmail

Co-organizer of the « Forum sur les poursuites d’études », IUT Nice Côte d’Azur (November 10, 2016);

Representative of the QLIO department at « Salon de l’étudiant », Palais des expositions, Nice (November 26, 2016).

Christelle Caillouet

Co-Responsible of QLIO Department, until February 2016.

Joanna Moulierac

Co-Responsible of the DUT Informatique en Alternance, Computer Science Department, from January 2014 to March 2016.

PhD : Guillaume Ducoffe, *Metric properties of large graphs* https://

PhD in progress : Nicolas Huin, *Energy efficient Software Defined Networks*, since Oct. 2014, Supervisors: Frédéric Giroire and Dino Lopez (I3S);

PhD in progress : William Lochet, *Forcing subdivisions in digraphs*, since Sept. 2015, Supervisors: Frédéric Havet and Stéphan Thomassé (ENS Lyon);

PhD in progress : Fionn McInerney, *Combinatorial Games in Graphs*, since Oct. 2016, Supervisor: Nicolas Nisse;

PhD in progress : Steven Roumajon, *Les déterminants de la compétitivité régionale : données microéconomiques et réseaux d’innovation*, since Nov. 2015, Supervisors: Patrick Musso (Gredeg)
and Frédéric Giroire;

PhD in progress : Andrea Tomassilli, *Diffusion of information on large dynamic graphs*, since Oct. 2016, Supervisors: Stéphane Pérennes and Frédéric Giroire.

Rohit Agarwal

Date: from Jul 2016 until Aug 2016

Institution: Univ. Nice Sophia Antipolis (France)

Supervisor: Nicolas Nisse

Theodoros Karagkioules

Date: until March 2016

Institution: NKUA, Athens (Greece)

Supervisor: Nicolas Nisse

Raul Wayne Teixeira Lopez

Date: from Sep 2016 until Nov 2016

Institution: UFC, Fortaleza (Brazil)

Supervisor: Frédéric Havet

Ioannis Mantas

Date: from Mar 2016 until Aug 2016

Institution: Univ. Nice Sophia Antipolis (France)

Supervisor: David Coudert

Simon Nivelle

Date: from Jun 2016 until Jul 2016

Institution: ENS Cachan (France)

Supervisor: Guillaume Ducoffe et Nicolas Nisse

Stefano Ponziani

Date: from Mar 2016 until Aug 2016

Institution: Univ. Nice Sophia Antipolis (France)

Supervisor: Guillaume Ducoffe et Frédéric Giroire

Konstantinos Priftis

Date: until March 2016

Institution: Univ. of Patras (Greece)

Supervisor: David Coudert

Panagiotis Pylarinos

Date: from Nov. 2016

Institution: NKUA, Athens (Greece)

Supervisor: David Coudert

Andrea Thomassilli

Date: from Mar 2016 until Aug 2016

Institution: Univ. Nice Sophia Antipolis (France)

Supervisor: Nicolas Huin et Frédéric Giroire

Vladyslav Zaika

Date: from Mar 2016 until Aug 2016

Institution: Univ. Nice Sophia Antipolis (France)

Supervisor: Nicolas Nisse

David Coudert :

Member of the PhD jury of Guillaume Ducoffe, Univ. Nice Sophia Antipolis, December 9, 2016;

Referee and member of the PhD jury of Mohamad Kanj, Univ. Rennes, December 20, 2016;

Frédéric Giroire:

Member of the PhD jury of Leonardo Linguaglossa, Université Paris Diderot (Paris 7), September 9, 2016.

Frédéric Havet :

Member of the PhD jury of G. Duvillié, Université Montpellier, October 7 2016.

Nicolas Nisse :

Referee and member of the PhD jury of Valentin Garnero, Université Montpellier, July 4 2016.

Referee and member of the PhD jury of Jean-Florent Raymond, Université Montpellier, November 18 2016.

Member of the PhD jury of Guillaume Ducoffe, Univ. Nice Sophia Antipolis, December 9, 2016;

Guillaume Ducoffe:

Fête de la Science: presented the stand "Introduction à l’algorithmique" at Valrose, Univ. Nice Sophia Antipolis, France, October 12nd, 2016.

Frédéric Havet:

Fête de la Science: co-organised the Village des Sciences at Vinon-sur-Verdon, France (November 10-14, 2016). F. Havet gave many talks and animated several stands during the whole week.

Semaine des Mathématiques : presented the stand “Les formes de largeur constantes” at Vinon sur Verdon (March 17, 2016)

Culture Science au Lycée : gave thé conference “Magie mathématique et binaire” at Lycée Caucadis Vitrolles (April 28, 2016) and the conferences “La magie du bonaire” and “La Science du Ballon de Football” at Lycée Caucadis Vitrolles (December 9, 2016).

Vendredis de la Science: conducted scientific workshops for school children (6-11 year old) on friday afternoon. Weekly in Januray-February and May-June 2016.

General audience conference : gave the conference “La Science du Ballon de Football” at Rians, Var, France (January 29, 2016).

Nicolas Nisse:

Fête de la Science: animated several stands during the Village des Sciences at Vinon-sur-Verdon, France (November 10-14, 2016).

Fête de la Science: animated several stands in Palais des Congrès de Juan-Les-Pins, October 22-23rd, 2016

Steven Roumajon:

Fête de la Science: presented the stand "Introduction à l'algorithmique" at Valrose, Univ. Nice Sophia Antipolis, France, October 12nd, 2016.