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 SDN (software defined networks), wdm, wireless (radio), satellite, 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 and transportation networks.

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, software defined 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. We 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.

The methods and tools used in our studies come from discrete mathematics and combinatorial optimization, and Coati contributes to their improvements. Also, Coati works on graph-decomposition methods and various games on graphs which are essential for a better understanding of the structural and combinatorial properties of the problems, but also for the design of efficient exact or approximate algorithms. We contribute to the modelling of optimization problems in terms of graphs, study the complexity of the problems, and then we investigate the structural properties of graphs that make these problems hard or easy. We exploit these properties in the design of algorithms in order to find the most efficient ways for solving the problems.

Coati also focuses on the theory of *directed graphs*. Indeed, graph theory can be roughly partitioned into two branches: the areas of undirected graphs and directed graphs. Even though both areas have numerous important applications, for various reasons, undirected graphs have been studied much more extensively than directed graphs. It is worth noticing that many telecommunication problems are modelled with directed graphs. Therefore, a deeper understanding of the theory of directed graphs will benefit to the resolution of telecommunication networks problems. For instance, the problem of finding disjoint paths becomes much more difficult in directed graphs and understanding the underlying structures of actual directed networks would help us to propose solutions.

Coati is mostly interested in telecommunications networks. We focus on the design and management of heterogeneous physical and logical 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.). However, the fields of Software Defined Networks and Network Function Virtualization are growing in importance in our studies.

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 collaborate with EP ABS (Algorithms Biology Structure) from Sophia Antipolis on problems from Structural Biology (see Section ). In the area of transportation networks, we have started a collaboration with SME Instant-System on dynamic car-pooling combined with multi-modal transportation systems. This collaboration will be strengthen in the near future with the support of an ANR project (starting January 2018).

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

Guillaume Ducoffe, former PhD student of Coati, is the recipient of an accessit to the PhD prize Graphes “Charles Delorme” 2017 for his PhD thesis entitled “Metric properties of large graphs”.

Frédéric Giroire and Joanna Moulierac are recipients of the Wilkes Award 2017 for the paper "Energy Efficient Content Distribution" (The Wilkes Award is given once a year to the authors of the best paper published in the volume of *The Computer Journal* from the previous year).

Keywords: Graph algorithmics - Distributed computing - Java - Graph processing

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.

In 2017 we have developed a multi-threaded shared-memory parallel version of the Bulk Synchronous Parallel framework. This new version uses advanced synchronization mechanisms and strategies to minimize the congestion of multiple threads working on the same graph. Using the NEF cluster (Inria Sophia Antipolis), this parallel version exhibits speed-ups up to 6.5 using 8 nodes (16 cores each) when computing a BFS on the 23 G edges Twitter graph sample.

Participants: Luc Hogie, Michel Syska and Nicolas Chleq

Partner: CNRS

Contact: Luc Hogie

*The high performance graph library for Java*

Keywords: Graph - Graph algorithmics - Java

Functional Description: Grph is an open-source Java library for the manipulation of graphs. Its design objectives are to make it portable, simple to use/extend, computationally/memory 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 programming solvers, a framework for distributed computing, etc.

Grph offers a very general model of graphs. Unlike other graph libraries which impose the user to first decide if he wants to deal with directed, undirected, hyper (or not) graphs, the model offered by Grph is unified in a general class that supports mixed graphs made of undirected and directed simple and hyper edges. Grph achieves great efficiency through the use of multiple code optimization techniques such as multi-core parallelism, caching, adequate data structures, use of primitive objects, exploitation of low-level processor caches, on-the-fly compilation of specific C/C++ code, etc. Grph attempts to access the Internet in order to check if a new version is available and to report who is using it (login name and hostname). This has no impact whatsoever on performance and security.

Participants: Aurélien Lancin, David Coudert, Issam Tahiri, Luc Hogie and Nathann Cohen

Contact: Luc Hogie

*SageMath*

Scientific Description: SageMath is a free open-source mathematics software system. 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.

Functional Description: SageMath is an open-source mathematics software initially created by William Stein (Professor of mathematics at Washington University). 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 four topics:
Firstly, we study the new network paradigms, Software-Defined Networks (SDN) and Network Function Virtualization (NFV). On the contrary to legacy networks, in SDN, 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. We then tackle the problem of placement of virtualized resources. We validated our algorithms on a real SDN platform

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 to 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. Also, we investigate in 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 entries 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

Hence, both simulations and experimental results suggest that Minnie can be safely deployed in real networks, providing compression ratios between 70% and 99%.

Energy aware routing aims at reducing the energy consumption of ISP networks. The idea is to adapt routing to the traffic load in order to turn off some hardware. However, it implies to make dynamic changes to routing configurations which is almost impossible with legacy protocols. The SDN paradigm bears the promise of allowing a dynamic optimization with its centralized controller.

In , , we propose SENAtoR, an algorithm to enable energy aware routing in a scenario of progressive migration from legacy to SDN hardware. Since in real life, turning off network equipments is a delicate task as it can lead to packet losses, SENAtoR provides also several features to safely enable energy saving services: tunneling for fast rerouting, smooth node disabling and detection of both traffic spikes and link failures.

We validate our solution by extensive simulations and by experimentation. We show that Minnie can be progressively deployed in a network using the SDN paradigm. It allows to reduce the energy consumption of ISP networks by 5 to 35% depending on the penetration of SDN hardware, while diminishing the packet loss rate compared to legacy protocols.

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. The challenge is then to efficiently provision the service chain requests, while finding the best compromise between the bandwidth requirements, the number of locations for hosting Virtual Network Functions (VNFs), and the number of chain occurrences.

We study optimization problems on various kinds of wireless networks.

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. We provide in 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 at each leaf in the tree a valid routing for the network is evaluated. Any such tree provides bounds 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, and we evaluate its computational efficiency.

Anytime and anywhere network access can be provided by Unmanned Aerial Vehicles (UAV) with air-to-ground and air-to-air communications using directional antennas for targets located on the ground. Deploying these Unmanned Aerial Vehicles to cover targets is a complex problem since each target should be covered, while minimizing (i) the deployment cost and (ii) the UAV altitudes to ensure good communication quality. We also consider connectivity between the UAVs and a base station in order to collect and send information to the targets, which is not considered in many similar studies. In , we provide an efficient optimal program to solve this problem and show the trade-off analysis due to conflicting objectives. We propose a fair trade-off optimal solution and also evaluate the cost of adding connectivity to the UAV deployment.

A wide range of social, technological and communication systems can be described as complex networks. Scale-free networks are one of the well-known classes of complex networks in which nodes degree follow a power-law distribution. The design of scalable, adaptive and resilient routing schemes in such networks is very challenging. In , we present an overview of required routing functionality, categorize the potential design dimensions of routing protocols among existing routing schemes and analyze experimental results and analytical studies performed so far to identify the main trends/trade-offs and draw main conclusions. Besides traditional schemes such as hierarchical/shortest-path path-vector routing, the article pays attention to advances in compact routing and geometric routing since they are known to significantly improve the scalability in terms of memory space. The identified trade-offs and the outcomes of this overview enable more careful conclusions regarding the (in-)suitability of different routing schemes to large-scale complex networks and provide a guideline for future routing research. This article concludes the European Project FP7 STREP EULER (2010-2014).

A routing *edge-forwarding index with respect to $R$* (or simply the forwarding index with respect to

Peer to peer networks are an efficient way to carry out video live streaming as the forwarding load is distributed among peers. These systems can be of two types: unstructured and structured. In unstructured overlays, the peers obtain the video in an opportunistic way. The advantage is that such systems handle churn well. However, they are less bandwidth efficient than structured overlays, and the control overhead has a non-negligible impact on the performance. In structured overlays, the diffusion of the video is made via an explicit diffusion tree. The advantage is that the peer bandwidth can be optimally exploited. The drawback is that the departure of peers may break the diffusion tree.

Coati is 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.

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.

Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More recently, hardness results for problems in P were established under reasonable complexity theoretic assumptions such as: Strong Exponential Time Hypothesis (SETH), 3SUM and All-Pairs Shortest-Paths (APSP). According to these assumptions, many graph theoretic problems do not admit truly subquadratic algorithms, nor even truly subcubic algorithms (Williams and Williams, FOCS 2010 and Abboud *et al.* SODA 2015 ). A central technique used to tackle the difficulty of the above mentioned problems is fixed-parameter algorithms for polynomial-time problems with *polynomial dependency* in the fixed parameter (P-FPT). This technique was rigorously formalized by Giannopoulou et al. (IPEC 2015) , . Following that, it was continued by Abboud *et al.* (SODA 2016) , by Husfeldt (IPEC 2016) and Fomin *et al.* (SODA 2017) , using the treewidth as a parameter. Applying this technique to *clique-width*, another important graph parameter, remained to be done.

The square of a given graph *et al.* (IWOCA'16) by showing that the squares of *cactus-block graphs* can be recognized in polynomial time. Our proof is based on new relationships between the decomposition of a graph by cut-vertices and the decomposition of its square by clique cutsets.
More precisely, we prove that the closed neighbourhoods of cut-vertices in

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.

In , we answer open questions of Verbeek and Suri on the relationships between Gromov hyperbolicity and the optimal stretch of graph embeddings in Hyperbolic space. Then, based on the relationships between hyperbolicity and Cops and Robber games, we turn necessary conditions for a graph to be Cop-win into sufficient conditions for a graph to have a large hyperbolicity (and so, no low-stretch embedding in Hyperbolic space). In doing so we derive lower-bounds on the hyperbolicity in various graph classes – such as Cayley graphs, distance-regular graphs and generalized polygons, to name a few. It partly fills in a gap in the literature on Gromov hyperbolicity, for which few lower-bound techniques are known.

In we study practical improvements for the computation of hyperbolicity in large graphs. Precisely, we investigate relations between the hyperbolicity of a graph *atoms*, that are the subgraphs output by the clique-decomposition invented by Tarjan and Leimer . We prove that the maximum hyperbolicity taken over the atoms is at most one unit off from the hyperbolicity of *exactly* the hyperbolicity of the input graph *linear-time* algorithm for computing the hyperbolicity of an outerplanar graph.

Convexity in graphs generalises the classical convexity in Euclidean spaces. The *hull-number* of a graph is the minimum number k such that there exists a set of k vertices whose convex hull is the graph. Computing the hull-number is NP-hard even in very restricted graph classes such as partial cubes (isometric subgraphs of hypercubes). One challenging question in this area is the status of the parameterized complexity of this problem. We further investigate the complexity of a more general problem.

The intent to show that the latter problem is LOGSNP-complete leads to several interesting questions and to the definition of the isometric hull, i.e., a smallest isometric subgraph containing a given set of vertices

For a (possibly infinite) fixed family of graphs

In an informal collaboration with Amadeus' members (A. Salch and V. Weber), we have studied the following problem. When an aircraft is approaching an airport, it gets a short time interval (called *slot*) that it can use to land. If the landing of the aircraft is delayed (because of bad weather, or if it arrives late, or if other aircrafts have to land first), it looses its slot and Air traffic controllers have to assign it a new slot. However, slots for landing are a scare resource of the airports and, to avoid that an aircraft waits too much time, Air traffic controllers have to regularly modify the assignment of the slots of the aircrafts. Unfortunately, for legal and economical reasons, Air traffic controllers can modify the slot-assignment only through specific kind of operations. The problem is then the following. Precisely, let *using* only augmenting paths of length *at most $k$*?

By Berge's theorem, finding a *maximum matching* in a graph relies on *the use* of *augmenting paths*. When no further constraint is added (*NP*-complete for any fixed *P*, for any *exactly* *NP*-complete for any fixed

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.

An algorithmic interpretation of tree/path-decomposition is the well known *graph searching* problem, where a team of searchers aims at capturing an intruder in a network, modeled as a graph.
All variants of this problem assume that any node can be simultaneously occupied by several searchers. This assumption may be unrealistic, e.g., in the case of searchers modeling physical searchers, or may require each individual node to provide additional resources, e.g., in the case of searchers modeling software agents.

We then study exclusive graph searching in a distributed setting.
Consider a set of mobile robots placed on distinct nodes of a discrete, anonymous, and bidirectional ring.
Asynchronously, each robot takes a snapshot of the ring, determining the size of the ring and 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.
This model of computation is known as *Look*-*Compute*-*Move*.
The computation 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 very weak assumptions. More precisely, we provide a full characterization (except for few pathological cases) of the initial configurations for which Gathering can be solved. The algorithm relies on the necessary assumption of the local-weak multiplicity detection. This means that during the Look phase a robot detects also whether the node it occupies is occupied by other robots, without acquiring the exact number.

For the exclusive searching, we characterize all (except for few pathological cases) aperiodic configurations from which the problem is feasible. We also provide some impossibility results for the case of periodic configurations.

We study several two-player games on graphs. Some of these games allow to model real-life applications. In the case of the Spy-game presented below, we propose a successful new approach by studying fractional relaxation of such games.

We define and study the following two-player game on a graph

In order to determine the smallest number of guards necessary for this task, we analyze in , , the game through a Linear Programming formulation and the *fractional strategies* it yields for the guards. We then show the equivalence of fractional and integral strategies in trees. This allows us to design a polynomial-time algorithm for computing an optimal strategy in this class of graphs.
Using duality in Linear Programming, we also provide non-trivial bounds on the fractional guard-number of grids and torus. We believe that the approach using fractional relaxation and Linear Programming is promising to obtain new results in the field of combinatorial games.

Coati 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.

We study various conditions that ensure a (di)graph to contain certain substructures.

A * $({k}_{1}+{k}_{2})$-bispindle* is the union of

Let

An *even pair* (resp. *odd pair*) in a graph is a pair of non-adjacent vertices such that every chordless path between them has even (resp. odd) length.
Even and odd pairs are important tools in the study of perfect graphs and were instrumental in the proof of the Strong Perfect Graph Theorem. We suggest that such pairs impose a lot of structure also in arbitrary, not just perfect graphs. To this end, we show in that the presence of even or odd pairs in graphs imply a special structure of the stable set polytope. In fact, we give a polyhedral characterization of even and odd pairs.

A graph

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

Towards the 1-2-3-Conjecture, the best-known result to date is due to Kalkowski, Karoński and Pfender, who proved that it holds when relaxed to 5-edge-weightings. Their proof builds upon a weighting algorithm designed by Kalkowski for a total version (where also the vertices are weighted) of the problem. In , we present new mechanisms for using Kalkowski's algorithm in the context of the 1-2-3 Conjecture. As a main result we prove that every 5-regular graph admits a 4-edge-weighting that permits to distinguish its adjacent vertices via their incident sums.

A colouring of a graph *properly connected* if every two vertices of *complexity* of computing the *proper connection number* (minimum number of colours in a properly connected colouring) for edge and vertex colourings, in undirected and directed graphs, respectively.
First we disprove some conjectures of Magnant et al. (2016) on characterizing the strong digraphs with *proper arc connection number* at most two. Then, we prove that deciding whether a given digraph has proper arc connection number at most two is NP-complete. Furthermore, we show that there are infinitely many such digraphs with no even-length dicycle.
We initiate the study of proper vertex connectivity in digraphs and we prove similar results as for the arc version. Finally, we present polynomial-time recognition algorithms for *bounded-treewidth* graphs and *bipartite* graphs with *proper edge connection number* at most two.

A graph is *locally irregular* if no two adjacent vertices have the same degree. The *irregular chromatic index*

An

An edge colouring of a graph

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

A particular interest was dedicated to grids as many processor networks have a grid topology. There are several types of standard regular infinite grids, in particular the hexagonal grids, the square grids, the triangular grids and the king grids. For such graphs

The Barát-Thomassen conjecture asserts that for every tree

A connected graph *arbitrarily partitionable* (AP for short) if for every partition *online arbitrarily partitionable* and *recursively arbitrarily partitionable* (OL-AP and R-AP for short, respectively), in which the subgraphs induced by a partition of *balloons*

An oriented graph is a directed graph without any directed cycle of length at most 2. An oriented clique is an oriented graph whose non-adjacent vertices are connected by a directed 2-path. To push a vertex

In the context of a conjecture of Erdős and Gyárfás, we consider in , for any *i.e.* with length a power of

For a fixed degree sequence

A very nice result of Barany and Lehel asserts that every finite subset

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 was 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 has firstly establish bounds on some classical graph parameters (e.g., clique number, stability number, chromatic number) for

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

Action Graphes, working group of GDR IM, CNRS.

Title: distributed ALgorithms for DYnamic NETworks

International Partner (Institution - Laboratory - Researcher):

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

Duration: 2013-2018

See also: https://

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 metropolitean area. We are both interested in theoretical results concerning the feasibility of computing graph properties, and by their practical implementation (using Sagemath) for our application and their diffusion in the scientific community. See the ALDYNET project web page for more details.

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

Universidade Federal do Ceará (Fortaleza, Brazil), ParGO team;

Universidade Estadual do Ceará (Fortaleza, Brazil), Prof. Leonardo Sampaio;

Univ. of Southern Denmark (Odense, Denmark), Prof. Jørgen Bang-Jensen;

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

Concordia Univ. (Montréal, Québec, Canada), Prof. Brigitte Jaumard.

Jørgen Bang-Jensen

University of Southern Denmark, Odense, Denmark. January 2017.

Ararat Harutyunyan

Université de Toulouse III, France. February 2017.

Takako Kodate

Tokyo Woman’s Christian University, Japan. From March 2017 until April 2017.

Claudia Linhares-Sales

Universidade Federal do Ceará, Fortaleza, Brazil. January 2017.

Joseph Peters

Scool of computing Science, Simon Fraser University, BC Canada. Since October 2017.

Leonardo Sampaio Rocha

Universidade Estadual do Ceará, Fortaleza, Brazil. June 2017.

Ana Shirley Ferreira Da Silva

Universidade Federal do Ceará, Fortaleza, Brazil. January 2017.

Karol Suchan

Universidad Adolfo Ibáñez, Chile. From February 2017 until March 2017.

Laurent Viennot

Inria Paris (EP Gang), France. February 2017.

Min-Li (Joseph) Yu

Univ. of the Fraser valley, Abbotsford, (BC), Canada. From March 2017 until April 2017.

Julien Bensmail

LaBRI, Université de Bordeaux, April 24-28 and October 9-13, 2017.

Christelle Caillouet

Reunion Island University, LIM Laboratory, October 20-November 19, 2017.

David Coudert

Gran Sasso Science Institute (GSSI), L'Aquila, Italy, April 19-21, 2017;

Concordia University, Montréal, Québec, Canada, July 1-14, 2017;

Univ. Adolfo Ibáñez and Univ. Chile, Santiago, Chile, in the context of Inria associated team AlDyNet, November 17-December 2, 2017.

Guillaume Ducoffe

Faculty of Mathematics and Informatics, University of Bucharest, January 18-August 31, 2017.

Frédéric Giroire

Department of Computer Science and Software Engineering, Condordia University, Montréal, Canada, October 11-24, 2017.

Frédéric Havet

Laboratoire ICube, Université de Strasbourg, November 8-10, 2017;

LABRI, Bordeaux, November 14-17, 2017.

William Lochet

LABRI, Université de Bordeaux, October 8-13, 2017;

LIRMM, Université de Montpellier, June 13-15, 2017.

Nicolas Nisse

LIF, Aix-Marseille Université, July 9-13, 2017;

Univ. Adolfo Ibáñez and Univ. Chile, Santiago, Chile, in the context of Inria associated team AlDyNet, November 17-December 2, 2017.

Fionn Mc Inerney

Université de Montréal, Montréal, Canada, July 3-August 4, 2017;

Univ. Adolfo Ibáñez and Univ. Chile, Santiago, Chile, in the context of Inria associated team AlDyNet, November 17-December 2, 2017.

Bruce Reed

IMPA, Unité CNRS Mixte, Rio de Janeiro, Brazil, January 1-March 24, 2017;

School of Computer Science, McGill University, November 1-December 31, 2017.

Andrea Tomassilli

Concordia University, Montréal, Canada, October 1-December 28, 2017.

Whole team

Journées JCALM (May 4-5, 2017) held in Sophia-Antipolis. Topic: Designs.

Christelle Caillouet, David Coudert

“Journées RESCOM 2017” of GDR RSD of CNRS, Sophia Antipolis, France, January 11-13, 2017.

Frédéric Havet

6th STINT meeting, Valgaudemar, France, July 5-7, 2017;

7th STINT meeting, Sophia Antipolis, France, December 4-6, 2017.

Frédéric Havet, Bruce Reed

2nd Cassidian Workshop, Cassis, France, May 14-20, 2017.

Frédéric Giroire, Joanna Moulierac

GreenDays@Sophia 2017: 8th French workshop on Network Energy efficiency, Université Côte d'Azur, Campus SophiaTech, Sophia Antipolis, June 26-27, 2017.

Bruce Reed

Co-Organizer 2017 Barbados Graph Theory Workshop, Holetown, Barbados, March 24-31, 2017.

David Coudert

Scientific Co-Chair of Track 7 “Cloud Computing and Data Center Management” of the 14th International Symposium on Pervasive Systems, Algorithms, and Networks (I-SPAN'17), Exeter, UK, June 21-23, 2017.

David Coudert

AlgoTel'17: Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications, Quiberon, France, May 30-June 2, 2017;

ONDM'17: International Conference on Optical Networking Design and Modeling, Budapest, Hungary, May 15-17, 2017;

IEEE ICC'17: IEEE International Conference on Communications, Paris, France, May 21-25, 2017;

IEEE Globecom'17: IEEE Global Communications Conference, Singapore, December 4-8, 2017.

Frédéric Havet

IX Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2017), Marseille, France, September 11-15, 2017;

19th Journées Graphes et Algorithmes (JGA 2017), Bordeaux, France, November 15-17, 2017.

Nicolas Nisse

Member of the Scientific Committee of GRASTA’17, 8th workshop on GRAph Searching, Theory & Applications, Anogia, Crete, Greece, April 10–13, 2017;

FCT’17: 21st International Symposium on Fundamentals of Computation Theory, Bordeaux, France, September 11-13, 2017.

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, Algorithms and Applications.

David Coudert

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

Frédéric Giroire

Journal of Interconnection Networks (World Scientific).

Frédéric Havet

Discrete Mathematics and Theoretical Computer Science.

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.

Julien Bensmail

Seminar of the Graphs and Optimisation team, LaBRI, Bordeaux (April 28, 2017): “On augmenting matchings via bounded-length augmentations”.

David Coudert

Seminar of the MAORE team, LIRMM, Montpellier (January 20, 2017): “Design of reliable fixed microwave backhaul networks”;

Joint ACP and GdR RO Summer School on Constraints and Operational Research, Porquerolles, France (September 18-22, 2017): “On the Flinders Hamiltonian Cycle Problem Challenge”;

Seminario del Doctorado en Ingeniera de Sistemas Complejos, Santiago, Chile (November 23, 2017): “On the Flinders Hamiltonian Cycle Problem Challenge”.

Guillaume Ducoffe

Logic seminar, University of Bucharest, Romania (March 2, 2017): “Treewidth vs. Treelength”;

Scientific seminar, West University of Timisoara, Romania (April 26, 2017): “Revisiting Preferential Attachment with applications to Twitter”;

International Workshop on Graphs, Networks and Digital Humanities, Bucharest, Romania (October 9, 2017): “Revisiting Preferential Attachment with applications to Twitter”.

Frédéric Giroire

Entretiens Jacques Cartier, Concordia University, Montréal, Canada (October 17-18, 2017): “Towards Energy Efficient Networks with SDN and Virtualization”;

SDN Day, IRT SystemX, Palaiseau, France (November 23, 2017): “Approximation algorithms for the Placement of Ordered Service Function Chains”.

Nicolas Nisse

Seminar of the ACRO team, LIF, Marseille (July 10, 2017): “Recovery of disrupted airline operations".

Luc Hogie, Michel Syska

Action GRAMINEES (GRaph data Mining in Natural, Ecological and Environnemental Sciences), journées Science des Données MaDICS (Masses de Données, Informations et Connaissances en Sciences), Marseille, France (June 23, 2017): “Bibliothèque de fouille de graphe”.

David Coudert

Member of the steering committee of *Pôle ResCom du GDR RSD du CNRS* since 2005, and co-chair since June 2017;

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

Frédéric Giroire

Member of the steering committee of *GT Energy of the GDR RSD du CNRS*.

Frédéric Havet

GT Graphes du GDR IM du CNRS;

Journées Graphes et Algorithmes (JGA);

Journées Combinatoire et Algorithmes du Littoral Méditerranéen (JCALM).

Jean-Claude Bermond

Expert for DRTT-MESR (Crédit impôt recherche (CIR et agréments)).

David Coudert

Expert for the Future and Emerging Technologies Open (FET-Open) European program (RIA Cut-off September 27, 2017);

Expert for “Haut Conseil de l'évaluation de la recherche et de l'enseignement supérieur” (HCERES).

Frédéric Giroire

Expert for ANR.

Frédéric Havet

Expert for ANR and NSERC.

Jean-Claude Bermond

Responsible for 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).

Christelle Caillouet

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

Elected member of I3S laboratory committee since December 2016;

Recruiting committee (comité de sélection) University of Lyon.

David Coudert :

President of “Comité de Sélection” SCIENCES / 27-PR-388, Université Nice-Sophia Antipolis, 2017;

Nominated member for Inria at the doctoral school STIC since September 2017;

Member of the “Comité de Suivi Doctoral” of Inria;

Member of the scientific council of Academy RISE (Networks, Information, Digital Society) of UCA

Frédéric Giroire :

Elected member of I3S laboratory committee since 2012 (reelected in December 2016);

In charge of the internships of stream UbiNet of Master 2 IFI, UNS.

Frédéric Havet :

Responsible of the ComRed Team of I3S.

Joanna Moulierac

Member of a “Comité de sélection” in Marseille, France, for the 27th section;

Member of the “Conseil de Département Informatique” of IUT Nice.

Nicolas Nisse

Elected member (deputy) of the “Comité de Centre” of Inria 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**

Julien Bensmail

*Recherche opérationnelle*, 82h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Systèmes de gestion de bases de donnés*, 86h ETD, Level L2, IUT Nice Côte d’Azur, UNS.

Christelle Caillouet

*Object-Oriented Programming*, 60h ETD, Level L1, IUT Nice Côte d’Azur, UNS.

Guillaume Ducoffe

*Introduction Programmation Java*, 9h ETD, Niveau L1, Polytech Nice Sophia.

Nicolas Huin

*Architecture des réseaux*, 21h ETD, Niveau L1, IUT de Nice Côte d'Azur, UNS;

*Programmation répartie*, 21h ETD, Niveau L2, IUT de Nice Côte d'Azur, UNS;

*Compléments d'algorithmique*, 21h ETD, Niveau L2, IUT de Nice Côte d'Azur, UNS.

Nicolas Nisse

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

Joanna Moulierac

*Networks*, 100h ETD, Niveau L1, IUT Nice Côte d'Azur, UNS;

*Algorithmics*, 30h ETD, Niveau L1, IUT Nice Côte d'Azur, UNS;

*Algorithmics*, 30h ETD, Niveau L2, IUT Nice Côte d'Azur, UNS.

Andrea Tomassilli

*Informatique théorique 2*, 24h, Niveau L3, Polytech Nice Sophia.

*Introduction to UNIX and Linux*, 12h, Niveau L3, Polytech Nice Sophia.

Michel Syska

*Operating Systems: Advanced Programming*, 90h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Data Structures and Algorithms*, 54h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Algorithmics*, 51h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Distributed Programming*, 51h ETD, Level L2, IUT Nice Côte d’Azur, UNS;

*Introduction to Algorithms and Complexity*, 30h ETD, Level L3, IUT Nice Côte d’Azur, UNS;

*IT foundations*, 26h ETD, Level L1, IUT Nice Côte d’Azur, UNS;

*Digital culture*, 10h 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;

*Hamiltonian Cycles*, 4h ETD, M2 MDFI, Aix-Marseille University, France.

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.

Stéphane Pérennes

*Calcul concurrent et distribué en Java*, 60h ETD, Level M1, Miage, Polytech Nice Sophia.

Nicolas Nisse

*Graph Algorithms*, 18h ETD, stream UbiNet of Master 2 IFI and Master RIF, UNS;

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

*Matching and Graph decompositions*, 4h ETD, M2 MDFI, Aix-Marseille University.

PhD: Nicolas Huin, *Energy efficient software defined networks* https://

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

PhD in progress: William Lochet, *Substructures in digraphs*, since September 2015. Co-supervisors: Frédéric Havet and Stéphan Thomassé (ÉNS Lyon).

PhD in progress: Yelena Yuditsky, School of Computer Science, McGill University. Supervisor: Bruce Reed.

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

PhD in progress: Thibaud Trolliet, *Exploring Trust on Twitter*, since October 2017. Co-supervisors: Arnaud Legout (DIANA) and Frédéric Giroire.

PhD (stopped for reorientation): Steven Roumajon, *Les déterminants de la compétitivité régionale : données microéconomiques et réseaux d'innovation*, from November 2015 until June 2017. Co-supervisors: Patrick Musso (Gredeg) and Frédéric Giroire.

Rohit Agarwal

Date: from March 2017 until August 2017

Institution: stream UbiNet of Master 2 IFI, Université Nice-Sophia Antipolis (France)

Supervisors: Frédéric Giroire

Subject: Random graph models for directed social graphs like Twitter

Eleni Batziou

Date: from November 2017 until May 2018

Institution: Master 2, National Technical University of Athens (Greece)

Supervisors: David Coudert

Subject: Enhancing urban mobility with shared on-demand services

Thibaut Blanc

Date: from May 2017 until August 2017

Institution: Licence 3, École Normale Supérieure de Rennes (France)

Co-supervisors: Julien Bensmail, Frédéric Havet

Subject: BMRN-colouring of digraphs

Samir Idwy

Date: from April 2017 until August 2017

Institution: Master 2, Institut National des Postes et Télécommunications (Morocco)

Supervisors: David Coudert

Subject: Transports collectifs personnalisés dans la ville

Lokesh Jain

Date: from June 2017 until August 2017

Institution: Master 2, Birla Institute of Technology and Science (India)

Context: Google Summer of Code (GSoC) 2017

Co-supervisors: David Coudert, Dmitrii Pasechnik (University of Oxford, UK)

Subject: Modular decomposition of graphs in Sagemath

Marko Oleksiyenko

Date: from March 2017 until August 2017

Institution: stream UbiNet of Master 2 IFI, Université Nice-Sophia Antipolis (France)

Co-supervisors: David Coudert, Nicolas Nisse

Subject: 2-mode itinerary computation

Panagiotis Pylarinos

Date: from November 2016 until May 2017

Institution: Master 2, National and Kapodistrian University of Athens (Greece)

Supervisors: David Coudert

Subject: Inclusion of dynamic ride-sharing in multimodal trip planning

Maria Spyrakou

Date: from June 2017 until August 2017

Institution: Master 2, National and Kapodistrian University of Athens (Greece)

Context: Google Summer of Code (GSoC) 2017

Co-supervisors: David Coudert, Dmitrii Pasechnik (University of Oxford, UK)

Subject: Modular decomposition of directed graphs in Sagemath

Thibaud Trolliet

Date: from February 2017 until July 2017

Institution: Master 2, École Normale Supérieure de Lyon (France)

Co-supervisors: Frédéric Giroire, Stéphane Pérennes

Subject: Modélisation du graphe des suivis de Twitter

Othmane Bensouda Korachi

Date: from November 2017 until December 2017

Institution: stream UbiNet of Master 2 IFI, UNS

Co-supervisors: Christelle Caillouet, Frédéric Giroire

Subject: Maintaining wireless sensor networks using drones and wireless power transfer

Laila Daanoun

Date: from November 2017 until December 2017

Institution: stream UbiNet of Master 2 IFI, UNS

Co-supervisors: Christelle Caillouet, Frédéric Giroire

Subject: Maintaining wireless sensor networks using drones and wireless power transfer

Mohamed Janati Idrissi

Date: from November 2017 until December 2017

Institution: stream UbiNet of Master 2 IFI, UNS

Co-supervisors: Christelle Caillouet, David Coudert

Subject: Mobile target covering for efficient aerial data gathering

Nirmal Vadakke Palangatt

Date: from November 2017 until December 2017

Institution: stream UbiNet of Master 2 IFI, UNS

Co-supervisors: David Coudert, Nicolas Nisse

Subject: Routing in multimodal networks with bicycles

Mykhailo Zima

Date: from November 2017 until December 2017

Institution: stream UbiNet of Master 2 IFI, UNS

Co-supervisors: David Coudert, Nicolas Nisse

Subject: Routing in multimodal networks with bicycles

Weilin Zhou

Date: from November 2017 until December 2017

Institution: stream UbiNet of Master 2 IFI, UNS

Co-supervisors: Frédéric Giroire, Joanna Moulierac

Subject: Optimization methods for network slicing

Jean-Claude Bermond

President of the jury for the 2017 award “Charles Delorme” for the best PhD thesis in graph theory (http://

Member of the jury Robertval (http://

David Coudert :

Referee and member of the PhD jury of Lorenzo Severini, GSSI, L'Aquila, Italy, April 20, 2017;

President of the PhD jury of Guillaume Perez, Université Côte d'Azur, September 29, 2017;

External referee in the PhD thesis monitoring committee of M. Amine Ait-Ouahmed, Université d'Avignon et des Pays de Vaucluse, October 27, 2017;

External referee for authorizing Fen Zhou to enroll in the HDR program, Université d'Avignon et des Pays de Vaucluse, November 2017.

Frédéric Giroire

Member of the PhD jury of Radu Carpa, ÉNS Lyon and Univ. Lyon, October 26, 2017;

Member of the PhD jury of Nicolas Huin, Université Côte d'Azur, September 28, 2017.

Frédéric Havet

Referee and member of the PhD jury of Lucas Pastor, Université Grenoble Alpes, November 23, 2017.

Nicolas Nisse

Member of the PhD jury of Pedro Montealegre, Univ. Orléans, February 28, 2017;

Member of the PhD jury of Sylvain Legay, Univ. Paris Saclay, March 1, 2017;

Referee and member of the PhD jury of Noël Gillet, Université Bordeaux, March 10, 2017;

Referee and member of the PhD jury of Antoine Naudin, Aix-Marseille Université, October 25, 2017.

Joanna Moulierac

“Directrice d'études” for the 1st-year students of IUT Nice Côte d'Azur, Département Informatique (since September 2017).

Jean-Claude Bermond

Gave a talk “50 years of passion trying to solve delectable problems about graphs and networks” on March 24 during a seminar C@fé ADSTIC organized by the ADSTIC (Doctoral Association of the SophiaTech campus).

Nathann Cohen and David Coudert

Article “le défi des 1001 graphes” relating how we addressed (and won) the Flinders Hamiltonian Cycle Project Challenge. Published in Interstices on December 12, 2017.

Frédéric Havet

Co-organised the “Village des Sciences” of Vinon-sur-Verdon, France, October 9-14, 2017. Gave many talks and animated several stands during the whole week;

Animated a stand “Mathémagie” at the “Village des Sciences” of Aix-en-Provence, October 8, 2017;

Organised the “Science Tour” at Rians, January 25-28, 2017. Animated several stands during the four days;

Gave the conferences “Beauty in Mathematics”, “Le métier de chercheur”, “La science du ballon de football” to five classes of the International School of Manosque, France, during the “Semaine des Mathématiques”, March 13-19, 2017;

Gave an interactive conference and animated stands about “Becs, pattes et plumes des oiseaux” and “ Nids des oiseaux” to four classes at Rians elementary school, France, January 9 and March 23, 2017;

Gave the conference “Élégance en Mathématiques” at Valgaudemar, France, July 6, 2017;

Frédéric Havet, Joanna Moulierac

Supervised the one-week internship of two 3eme schoolboys.

Nicolas Nisse

Co-organized (with “Les petits débrouillards”, see http://

Animated, during “Fête de la Science”, several stands during the “Village des Sciences” at Vinon-sur-Verdon, France, October 10-13, 2017;

Animated, during “Fête de la Science”, several stands in Palais des Congrès de Juan-Les-Pins, October 7-8, 2017;

Realization of series of posters for scientific popularization , , , ;

Member of MASTIC (Médiation et Animation scientifiques Inria, see https://

Frédéric Havet, Joanna Moulierac, Nicolas Nisse

Involved in the GALEJADE project supported by Fondation Blaise Pascal. The main objective of this project is to develop a series of games for initiating schoolchildren to graphs and algorithms, and to put them in a pedagogical kit and on the web.