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 Univ. Côte d'Azur.
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 prototype and more advanced software, and in the contribution to large open source software such as Sagemath.

Since its creation in 2013, the objectives of Coati are to conduct fundamental research in Discrete Mathematics, Graph Theory, Digraph Theory, Algorithms and Operations Research, and to use these tools for studying specific network optimization problems. Notice that we are mostly interested in telecommunications networks. However, our expertise can be applied to solve many other problems in various areas (transport, biology, resource allocation, social sciences, smart-grids, speleology, etc.) and we collaborate with teams of these other domains. Coati also contributes to the development of software components in order to validate proposed algorithms and to boost their dissemination.

The research program of Coati is therefore structured as follows.

Note also that beside our research activity, we are deeply involved in the dissemination of our domain towards a general public.

Coati is mostly interested in telecommunications networks but also in the network structure appearing in social, molecular and transportation 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). However, the fields of Software Defined Networks and Network Function Virtualization are growing in importance in our studies. In all these networks, we study routing algorithms 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 collaborate with experts of some of these domains.

For instance, we collaborate with project-team ABS (Algorithms Biology Structure) from Sophia Antipolis on problems from Structural Biology (co-supervision of a PhD student). In the area of transportation networks, we collaborate with SMEs Benomad and Instant-System on dynamic car-pooling combined with multi-modal transportation systems in the context of ANR project Multimod started in January 2018. We collaborate with SME MillionRoads since October 2019 on the modeling and exploration of the HumanRoads database that gathers more than 100 million curriculums (studies and career paths of persons). Last, we have started a collaboration with GREDEG (Groupe de Recherche en Droit, Economie et Gestion, Université Côte d'Azur) and the SKEMA business school on the analysis of the impact of competitive funding on the evolution of scientific collaboration networks.

Modeling of a database linking users to their studies and careers in the form of a graph. Algorithms for graphs associated with the queries made (of the type: number of users who have completed a given curriculum, distribution of careers following a given curriculum, distribution of curriculums preceding a given career, etc.). Scaling for a database of >100 million users.

In addition, Neo4j implemetations of various algorithms tested on the HumanRoads data.

Idawi is a middleware for the development and experimentation of distributed algorithms. It boasts a very general and flexible multi-hop component-oriented model that make it applicable in many contexts such as parallel and distributed computing, cloud, Internet of Things (IOT), P2P networks, etc. Idawi components can be deployed anywhere a SSH connection is possible. They exhibit services which communicate with each other via explicit messaging. Messages and be sent in either synchronously or asynchronously, and they can be handled in either procedural (with the optional use of futures) or reactive (event-driven) fashion. In the latter case, multi-threading is used to maximize both speed and number of components in the system. Idawi message transport is done via TCP, UDP, SSH or shared-memory.

Idawi is a synthesis of the past developments of the COATI Research group in the field of graph algorithms for big graphs, and it is designed to be useful to the current and future Research project of COATI and KAIROS groups.

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 the following topics: Firstly, we study Network Function Virtualization (NFV) and how to embed them in public clouds. We also study the reconfiguration of network slices within 5G networks. Secondly, we study the optimization of LoRa networks. We propose a new analytic model to better evaluate the capacity of a single LoRaWAN cell and an optimization model to maximize the minimum packet delivery rate of every IoT node in the network. Thirdly, we pursued our study of distributed link scheduling in wireless networks. Finally, we investigate on the placement of drones for maximizing the coverage of a landscape by drones in order to localize targets or collect data from sensors.

Recent advances in networks such as Software Defined Networking (SDN) and Network Function Virtualization (NFV) are changing the way network operators deploy and manage Internet services. On the one hand, SDN introduces a logically centralized controller with a global view of the network state. On the other hand, NFV enables the complete decoupling of network functions from proprietary appliances and runs them as software applications on general purpose servers. In such a way, network operators can dynamically deploy Virtual Network Functions (VNFs). SDN and NFV, both separately, bring to network operators new opportunities for reducing costs, enhancing network flexibility and scalability, and shortening the time-to-market of new applications and services. Moreover, the centralized routing model of SDN jointly with the possibility of instantiating VNFs on demand may open the way for an even more efficient operation and resource management of networks. For instance, an SDN/NFV-enabled network may simplify the Service Function Chain (SFC) deployment and provisioning by making the process easier and cheaper. We addressed several questions in this context.

In 62, 63, 64 we address a cost minimization problem encountered by network operators subscribing to public cloud offers to embed network functions. The diversity of offers, in terms of resource capacity and price, makes it difficult to find the optimal combination of offers that meets all needs at the lowest cost. We propose to solve this issue with an algorithm designed to help a network operator to select the best combination of offers (in terms of price) to reserve the virtual machines needed to support a set of network services. We analyze the computation time of our solution against various metrics, and estimate the cost savings compared to a traditional resource provision scheme or an unplanned resource rental strategy. Finally we evaluate the opportunity for a network operator to build its own datacenter, considering the existence of offers from public clouds.

In 55, we consider the problem of network slice reconfiguration without interruption. A network slice can be seen as a virtual network embedded on the physical topology, with some VNFs placed in specific nodes. As an example, a simplified network slice could be an SFC. Reconfiguring from time to time network slices allows to reduce the network operational costs and to increase the number of slices that can be managed within the network. However, it impacts users' Quality of Service during the reconfiguration step. To solve this issue, we study solutions implementing a make-before-break scheme. We propose new models and scalable algorithms (relying on column generation techniques) that solve large data instances in few seconds.

In 61 we propose and implement a new placement module for distributed emulation of SDN/NFV emulation. To handle the ever growing demand of resource intensive experiments distributed, network emulation tools such as Mininet and Maxinet have been proposed. They automatically allocate experimental resources. However, we have shown that resources are poorly allocated, leading to resource overloading and hence to dubious experimental results. Our new algorithms take into account both link and node resources and minimize the number of physical hosts needed to carry out the emulation. Through extensive numerical evaluations, simulations, and actual experiments , we show that our placement methods outperform existing ones and allowing to re-establish trust in experimental results.

In 48, 60, we consider the problem of evaluating the capacity of a LoRaWAN cell. Previous analytical studies investigated LoRaWAN performance in terms of the Packet Delivery Ratio (PDR) given a number of devices around a gateway and its range. We improve the model for PDR by taking into consideration that the following two events are dependent: successful capture during a collision and successful frame decoding despite ambient noise. We consider a realistic traffic model in which all devices generate packets with the same inter-transmission times corresponding to the duty cycle limitation at the highest SF, regardless of the distance to the gateway. Based on the developed model, we optimize the Spreading Factor (SF) boundaries to even out PDR throughout the cell. We validate the analytical results with simulations, compare our model with previous work, and experimentally validate the hypothesis of Rayleigh fading for the LoRa channel. The important conclusion from our results is that a LoRa cell can handle a relatively large number of devices. We also show that there is practically no inter-SF interference (cross interference between transmissions with different SFs): interference from higher SFs comes from nodes located farther away, so they face greater attenuation and thus, they do not interfere with lower SF nodes.

In 47, we propose an optimization model for single-cell LoRaWAN planning which computes the limit range of each spreading factor (SF) in order to maximize the minimum packet delivery ratio (PDR) of every node in the network. It allows to balance the opposite effects of attenuation and collision of the transmissions and guarantee fairness among the nodes. We show that our optimization framework improves the worst PDR of the nodes by more than 13 percentage points compared to usual SF boundaries based on SNR threshold. A study of the tradeoff between precision and resolution time of the model shows its effectiveness even with a small number of possible distance limits, and its scalability when the node density increases.

In 29, we investigated distributed transmission scheduling in wireless networks. Due to interference constraints, “neighboring links” cannot be simultaneously activated, otherwise transmissions will fail. We consider any binary model of interference and use a model described by Bui, Sanghavi, and Srikant in 86, 92. We assume that time is slotted and during each slot there are two phases: one control phase in which a link scheduling algorithm determines a set of non interfering links to be activated, and a data phase in which data is sent through these links. We assume random arrivals on each link during each slot, so that a queue is associated to each link. We design the first fully distributed local algorithm with the following properties: it works for any arbitrary binary interference model; it has a constant overhead (independent of the size of the network and the values of the queues), and it does not require any knowledge of the queue-lengths. We prove that this algorithm gives a maximal set of active links, where for any non-active link there exists at least one active link in its interference set. We also establish sufficient conditions for stability under general Markovian assumptions. Finally, the performance of our algorithm (throughput, stability) is investigated and compared via simulations to that of previously proposed schemes.

In 28, we study the problem of gossiping with neighboring interference constraint in radio chain networks. Gossiping (also called total exchange information) is a protocol where each node in the network has a message and is expected to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and efficient algorithms that attain this makespan. We focus on the case where the transmission network is a chain (directed path or line) network. We consider synchronous protocols where it takes one unit of time (step) to transmit a unit-length message. During one step, a node receives at most one message only through one of its two neighbors. We assume that during one step, a node cannot be both a sender and a receiver (half duplex model). Moreover we have neighboring interference constraints under which a node cannot receive a message if one of its neighbors is sending. A round consists of a set of non-interfering (or compatible) calls and uses one step. We completely solve the gossiping problem for

The use of autonomous unmanned aerial vehicles (UAVs) or drones has emerged to efficiently collect data from mobile sensors when there is no infrastructure available. The drones can form a flying ad-hoc network through which the sensors can send their data to a base station at any time.

In 53, we present a mixed integer linear program to find the drones’ optimal trajectories to form and maintain this network through time while minimizing their movements and energy consumption. Furthermore we analyze the trade-off between distance and energy, where increasing the drones’ mobility can reduce their energy consumption, and derive a fair trade-off optimal solution to balance the two opposite objectives.

In 46, we propose VESPA, a distributed algorithm using only one-hop information of the drones, to discover targets with unknown location and auto-organize themselves to ensure connectivity between them and the sink in a multi-hop aerial wireless network. We prove that connectivity, termination and coverage are preserved during all stages of our algorithm, and we evaluate the algorithm performances through simulations. Comparison with a prior work shows the efficiency of VESPA both in terms of discovered targets and number of used drones.

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.

During the last decade, metric properties of the bags of tree decompositions of graphs have been studied. 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 32, we answer open questions of Dragan et al. 87, 88 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 (or more generally, a triangle-free graph, resp., a

The length of a tree-decomposition of a graph is the maximum distance between two vertices of a same bag of the decomposition. The treelength of a graph is the minimum length among its tree-decompositions. Treelength of graphs has been studied for its algorithmic applications in classical metric problems such as Traveling Salesman Problem or metric dimension of graphs and also, in compact routing in the context of distributed computing. Deciding whether the treelength of a general graph is at most 2 is NP-complete (graphs of treelength one are precisely the chordal graphs), and it is known that the treelength of a graph cannot be approximated up to a factor less than

In 81, we first fully describe the treelength of melon graphs (set of pairwise internally disjoint paths linking two vertices), showing that, even in such a restricted graph class, the expression of the treelength is not trivial. Then, we show that treelength can be approximated up to a factor

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

We have continued the study of the eternal domination game on strong grids. Cartesian grids have been vastly studied with tight bounds for small grids such as

In 33, we adapt the techniques of 90 to prove that the eternal domination number of strong grids is upper bounded by

In 35, we prove that, for all

In the Spy game played on a graph

In the localization game, introduced by Seager in 2013, an invisible and immobile target is hidden at some vertex of a graph

In 24, we address the generalization of this game where metric dimension of a graph.
Precisely, given a graph Localization problem asks whether there exists a strategy to locate a target hidden in NP-complete for every fixed Localization problem is NP-complete in trees when i.e., an algorithm that computes in time Localization problem in trees in polynomial time if

We also consider some of these questions in the context where, upon probing the vertices,
the relative distances to the target are retrieved.
This variant of the problem generalizes the notion of the centroidal dimension of a graph.

Since games and puzzles have been studied under a computational lens, researchers unearthed a rich landscape of complexity results showing deep connections between games and fundamental problems and models in computer science. Complexity of Games (CoG, https://

Kingdomino is a board game designed by Bruno Cathala and edited by Blue Orange since 2016. The goal is to place

The sidetracks-based (SB) algorithm which is currently the fastest solution. In this work, we propose two improvements of this algorithm.
In 39, 40, 70, we first show how to speed up the SB algorithm using dynamic updates of shortest path trees. We did experiments on some road networks of the 9th DIMAC'S challenge with up to about half a million nodes and one million arcs. Our computational results show an average speed up by a factor of 1.5 to 2 with a similar working memory consumption as SB. We then propose a second algorithm enabling to significantly reduce the working memory at the cost of an increase of the running time (up to two times slower). Our experiments on the same data set show, on average, a reduction by a factor of 1.5 to 2 of the working memory.

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose in 54, 56 a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-world network. The main idea is to invert the recurrence equation commonly used to compute the degree distribution in order to find a convenient attachment function for node connections-commonly chosen as linear. We compute this attachment function for some classical distributions, as the power-law, broken power-law, geometric and Poisson distributions. We also use the model on an undirected version of the Twitter network, for which the degree distribution has an unusual shape.

In 65, 66, we study the clustering of directed social graphs. The clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be of great interest to describe the characteristics of a social graph. In fact, the clustering coefficient is adapted for a graph in which the links are undirected, such as friendship links (Facebook) or professional links (LinkedIn). For a graph in which links are directed from a source of information to a consumer of information, it is no longer adequate. We show that former studies have missed much of the information contained in the directed part of such graphs. We thus introduce a new metric to measure the clustering of a directed social graph with interest links, namely the interest clustering coefficient. We compute it (exactly and using sampling methods) on a very large social graph, a Twitter snapshot with 505 million users and 23 billion links. We additionally provide the values of the formerly introduced directed and undirected metrics, a first on such a large snapshot. We exhibit that the interest clustering coefficient is larger than classic directed clustering coefficients introduced in the literature. This shows the relevancy of the metric to capture the informational aspects of directed graphs.

Spectral techniques have proved amongst the most effective approaches to graph clustering. However, in general they require explicit computation of the main eigenvectors of a suitable matrix (usually the Laplacian matrix of the graph). Recent work (e.g., Becchetti et al., SODA 2017 84) suggests that observing the temporal evolution of the power method applied to an initial random vector may, at least in some cases, provide enough information on the space spanned by the first two eigenvectors, so as to allow recovery of a hidden partition without explicit eigenvector computations. While the results of Becchetti et al. apply to perfectly balanced partitions and/or graphs that exhibit very strong forms of regularity, we extend their approach to graphs containing a hidden

In 41, we investigate opinion dynamics in multi-agent networks when a bias toward one of two possible opinions exists; for example, reflecting a status quo vs a superior alternative. Starting with all agents sharing an initial opinion representing the status quo, the system evolves in steps. In each step, one agent selected uniformly at random adopts the superior opinion with some probability

The election control problem through social influence asks to find a set of nodes in asocial network of voters to be the starters of a political campaign aiming at supporting a given target candidate. Voters reached by the campaign change their opinions on the candidates.The goal is to shape the diffusion of the campaign in such a way that the chances of victory of the target candidate are maximized. Previous work shows that the problem can be approximated within a constant factor in several models of information diffusion and voting systems, assuming that the controller, i.e., the external agent that starts the campaign, has full knowledge of the preferences of voters. However this information is not always available since some voters might not reveal it. In 38, we relax this assumption by considering that each voter is associated with a probability distribution over the candidates. We then propose two models in which, when an electoral campaign reaches a voter, this latter modifies its probability distribution according to the amount of influence it received from its neighbors in the network. We then study the election control problem through social influence on the new models: In the first model, under the Gap-ETH, election control cannot be approximated within a factor better than

Given an underlying graph, we consider the following dynamics: Initially, each node locally chooses a value in

The survey 17 provides an in-depth algorithmic perspective on emergent complexity. Roughly, this area aims to characterize non-trivial emergent properties of complex systems, composed of large numbers of relatively simple agents, which can cooperate to express complex global behaviours. Interestingly, over the past two decades, fundamental processes such as consensus or opinion-formation dynamics have been studied independently by different research communities: for instance, in the Distributed Computing community, these dynamics have been studied in the context of population protocols via discrete-time analysis, whereas, in the Control and Optimization community, similar (or even identical) dynamics have been analyzed via continuous-time processes. This survey provides a unified view of these results, along with the mathematical background to understand and differentiate the underlying results.

Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove in 49 a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the protocol. Using this reduction, we get, among other applications, the first logarithmic lower bound on the number of rounds needed to achieve Consensus in the uniform GOSSIP model on the complete graph. The lower bound is tight and, in this model, Consensus and Broadcast are equivalent. We then turn to distributed models with noisy communication channels that have been studied in the context of some bio-inspired systems. In such models, only one noisy bit is exchanged when a communication channel is established between two nodes, and so one cannot easily simulate a noiseless protocol by using error-correcting codes. An

We analyze in 52 the binary-state (either

In several real Multi-Agent Systems (MAS), it has been observed that only weaker forms ofmetastable consensus are achieved, in which a large majority of agents agree on some opinion while other opinions continue to be supported by a (small) minority of agents. In 67, we take a step towards the investigation of metastable consensus for complex (non-linear) opinion dynamics by considering the famous Undecided dynamics in the binary setting, which is known to reach consensus exponentially faster than the Voter dynamics. We propose a simple form of uniform noise in which each message can change to another one with probability p and we prove that the persistence of a metastable consensus undergoes a phase transition for stubborn way.

It follows from the Marcus-Spielman-Srivastava proof of the Kadison-Singer conjecture that if

In 50, we study parallel Load Balancing protocols for a client-server distributed model defined as follows. There is a set

Motivated by the Lévy flight foraging hypothesis – the premise that the movement of various animal species searching for food resembles a Lévy walk – we study the search efficiency of parallel Lévy walks on the infinite 2-dimensional grid. We assume that

Coati studies theoretical problems in graph theory. If some of them are directly motivated by applications,
others are more fundamental.

We are putting an effort on understanding better directed graphs (also called digraphs) and partitioning problems, and in particular colouring problems. We also try to better the understand the many relations between orientations 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.

In distinguishing labelling problems, the general goal is, given a graph, to label some of its elements so that some pairs of elements can be distinguished accordingly to some parameter computed from the labelling. Note that this description involves many parameters that can be played with, such as the set of elements to be labelled, the set of labels to be assigned, the set of elements to be distinguished, and the distinguishing parameter computed from the labelling. A notable example is the so-called 1-2-3 Conjecture, which asks whether almost all graphs can have their edges labelled with 1,2,3 so that every two adjacent vertices are distinguished accordingly to their sums of incident labels.

We have recently obtained a number of results, related both to the 1-2-3 Conjecture and related problems. These results stand both as notable progress towards some open questions, and as new problems of independent interest.

In a series of works, namely 45, 74, 75, 76, we have introduced and studied optimisation variants of the 1-2-3 Conjecture, our main intent being to understand better some of the core mechanisms and motivations behind the conjecture.

Namely, the 1-2-3 Conjecture is related to an optimisation problem where one aims at making any graph

One such side question is about proper labellings assigning only a few large labels. In particular, regarding the 1-2-3 Conjecture, an interesting question is about the importance of label 3, in the sense that, perhaps, in general labels 1 and 2 are almost enough to label any graph. Note that previous works on the topic have highlighted that graphs requiring all labels

In two works, namely 23, 26, we have studied two generalisations of distinguishing labelling problems to directed graphs (digraphs). In 23, we completely solved a peculiar variant of the 1-2-3 Conjecture in digraphs, where one is asked to design 3-labellings where, for every arc

In 26, we have studied directed variants of a related problem, called the AVD Conjecture, which is, in essence, a kind of 1-2-3 Conjecture where the labels assigned to the edges must form a proper edge-colouring (i.e., no two adjacent edges must be assigned a same label). Inspired from the existing directed variants of the 1-2-3 Conjecture, we have introduced a few directed variants of the AVD Conjecture, leading to interesting conjectures that we have partly solved.

In 31, we considered a variant in which we both orient and give weight to the edges of a graph. A weighted orientation of a graph arc-weighting of in-weight of a vertex semi-proper orientation is a weighted orientation such that two adjacent vertices have different in-weights.
The semi-proper orientation number of a graph optimal if

Given a system

A strong edge-colouring of an undirected graph

In 20, we initiate the study of the strong chromatic index of 1-planar graphs, which are those graphs that can be drawn on the plane in such a way that every edge is crossed at most once. We provide constructions of 1-planar graphs with maximum degree

A signed graph

Homomorphisms of signed graphs have been attracting growing attention in the last decades, especially due to their strong connections to the theories of graph coloring and graph minors.
These homomorphisms have been particularly studied through the scope of the signed chromatic number.
In 72, we provide new results and bounds on the signed chromatic number of several families of signed graphs (planar graphs, triangle-free planar graphs,

A simple signed graph

A graph

On the one hand, we consider algorithmic aspects of AP graphs, which received some attention in previous works.
We first establish the NP-hardness of the problem of partitioning a graph into connected subgraphs following a given sequence, for various new graph classes of interest.
We then prove that the problem of deciding whether a graph is AP is in NP for several classes of graphs, confirming a conjecture of Barth and Fournier for these.

On the other hand, we consider the weakening to APness of sufficient conditions for Hamiltonicity. While previous works have suggested that such conditions can sometimes indeed be weakened, we here point out cases where this is not true. This is done by considering conditions for Hamiltonicity involving squares of graphs, and claw- and net-free graphs.

A (undirected) graph is locally irregular if no two of its adjacent vertices have the same degree. A decomposition of a graph

In 21, we study the decomposability of degenerate graphs with low degeneracy. Our main result is that decomposable

In the recent study of crossing numbers, drawings of graphs that can be extended to an arrangement of pseudolines (pseudolinear drawings) have played an important role as they are a natural combinatorial extension of rectilinear (or straight-line) drawings. A characterization of the pseudolinear drawings of

A well-known conjecture of Erdős and Sós states that every graph with average degree exceeding

Let inversion of a set inversion number of

We then consider the complexity of deciding whether

An

The metric dimension

In 25, we study, for particular graph families, the maximum metric dimension over all strongly-connected orientations, by exhibiting lower and upper bounds on this value. We first exhibit general bounds for graphs with bounded maximum degree. In particular, we prove that, in the case of subcubic

The (directed) metric dimension of a digraph

We collaborate with experts in various areas (transport, bio-informatics, e-health, etc.). In this section, we present the results we have obtained in the context of these collaborations.

A major problem in structural biology is the characterization of low resolution structures of macro-molecular assemblies. One subproblem of this very difficult question is to determine the plausible contacts between the subunits (e.g. proteins) of an assembly, given the lists of subunits involved in all the complexes. This problem can be conveniently modelled by graphs and hypergraphs, and we collaborate with project-team ABS in order to better understand its computational complexity.

Let

Brain atlases are central objects in network neuroscience, where the interactions between different brain regions are modeled as a graph called connectome. In structural connectomes, nodes are parcels from a predefined cortical atlas and edges encode the strength of the axonal connectivity between regions measured via diffusion Magnetic Resonance Imaging (MRI) tractography. In collaboration with project-team ATHENA, we provided in

82a novel perspective on the evaluation of brain atlases by modeling it as a network alignment problem, with the goal of tackling the following question: given an atlas, how robustly does it capture the network topology across different subjects? To answer such a question, we introduce two novel concepts arising as natural generalizations of previous ones. First, the graph Jaccard index (GJI), a graph similarity measure based on the well-established Jaccard index between sets; the GJI exhibits natural mathematical properties that are not satisfied by previous approaches. Second, we devise WL-align, a new technique for aligning connectomes obtained by adapting the Weisfeiler-Lehman (WL) graph-isomorphism test. We validated the GJI and WL-align on data from the Human Connectome Project database, inferring a strategy for choosing a suitable parcellation for structural connectivity studies. Code and data are publicly available.

In order to express parallelism, parallel sparse direct solvers take advantage of the elimination tree to exhibit tree-shaped task graphs, where nodes represent computational tasks and edges represent data dependencies. One of the pre-processing stages of sparse direct solvers consists of mapping computational resources (processors) to these tasks. The objective is to minimize the factorization time by exhibiting good data locality and load balancing. The proportional mapping technique is a widely used approach to solve this resource-allocation problem. It achieves good data locality by assigning the same processors to large parts of the elimination tree. However, it may limit load balancing in some cases. In

57,

83, we propose a dynamic mapping algorithm based on proportional mapping. This new approach, named Steal, relaxes the data locality criterion to improve load balancing. In order to validate the newly introduced method, we perform extensive experiments on the PaStiX sparse direct solver. It demonstrates that our algorithm enables better static scheduling of the numerical factorization while keeping good data locality.

The recent push towards test automation and test-driven development continues to scale up the dimensions of test code that needs to be maintained, analyzed, and processed side-by-side with production code. As a consequence, on the one side regression testing techniques, e.g., for test suite prioritization or test case selection, capable to handle such large-scale test suites become indispensable; on the other side, as test code exposes own characteristics, specific techniques for its analysis and refactoring are actively sought. In

51, we propose JTeC, a large-scale dataset of test cases that researchers can use for benchmarking the above techniques or any other type of tool expressly targeting test code. JTeC collects more than 2.5M test classes belonging to 31K+ GitHub projects and summing up to more than 430 Million SLOCs of ready-to-use real-world test code.

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

Summary:
Directed graphs (digraphs) are much less understood than undirected graphs. Many, seemingly very
simple questions remain unsolved for digraphs while the analogous problem for undirected graphs
is trivial. At the same time digraphs are a very important modelling tool for practical
applications and so a better undestanding of their structure is important. The purpose of DISCO
is to advance knowledge on fundamental problems on digraphs, including splitting a digraph into
smaller pieces with given properties, problems regarding disjoint paths and trees, finding small
certificates for given properties, such as strong spanning subdigraphs with few arcs. The later
is important for speeding up certain algorithms.

Through a concerted effort we expect to obtain important results which will lead to a better undestanding of fundamental questions about the structure of digraphs. The participants will meet regularly both in France and in Denmark to work on carefully selected problems.

Members of Coati are involved in the working group RESCOM (Réseaux de communications) of GDR RSD, CNRS
(http://

We are also involved in the working group "Energy" of GDR RSD (http://

Members of Coati are involved in the working group "Graphes" of GDR IM, CNRS.
(http://

Members of Coati are involved in the working group GRAMINEES (GRaph data Mining in Natural, Ecological and Environnemental Sciences) of GDR MADICS (Masses de Données, Informations et Connaissances en Sciences).
(http://

Members of COATI have reviewed numerous manuscripts submitted to national and international conferences, including:

AAMAS'20, ALGOS'20, AlgoTel'20, CoRes'20, ESA'20, EvoApplications'20, ICALP'20, ICNC'20, IEEE Globecom'20 IEEE ICC'20, IEEE WiSARN'20, IJCAI'20, IWOCA'20, MFCS'20, MobiWis'20, ONDM'20, OPODIS'20, PODC'20, ROADEF'20, SPAA'20, WG'20.

Members of COATI have reviewed numerous manuscripts submitted to international journals, including:

ACM Transactions on Algorithms (TALG), Ad Hoc Networks, Advances in Combinatorics, Algorithmica, Applied Network Science, Computer Communications (ComCom) Computer Networks (COMNET), Computers & Operations Research (COR), Discrete Applied Mathematics (DAM), Discrete Mathematics and Theoretical Computer Sciences (DMTCS), Discussiones Mathematicae Graph Theory, Distributed Computing, European Journal of Combinatorics, European Journal of Operational Research (EJOR), IEEE Communication Letters, IEEE Journal of Intelligent Transport, IEEE Networking Letters, IEEE Transactions on Green Communications and Networking (TGCN), IEEE Transactions on Mobile Computing (TOMC), IEEE Transactions on Signal Processing, IEEE/ACM Transactions on Networking (ToN), IEEE/OSA Journal of Optical Communications and Networking (JOCN), INFORMS Journal on Computing, Journal of Advanced Transportation (Hindawi), Journal of Combinatorial Optimization, Journal of Graph Theory (JGT), MDPI Applied Sciences, PLOS One, The Computer Journal, Transactions on Mobile Computing.

Members of Coati have for more that 1320 hours (ETD) this year: