Chalopin, Jérémie 1980
Overview
Works:  17 works in 27 publications in 2 languages and 102 library holdings 

Roles:  Author, Editor, Opponent, Thesis advisor, Contributor, Organizer of meeting 
Classifications:  QA166, 511.5 
Publication Timeline
.
Most widely held works by
Jérémie Chalopin
Weakly modular graphs and nonpositive curvature by
Jérémie Chalopin(
Book
)
9 editions published between 2020 and 2021 in English and held by 67 WorldCat member libraries worldwide
"This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various "nonpositive curvature" and "localto global" properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a farreaching common generalization of median graphs (and more generally, of modular and orientable modular graphs), Helly graphs, bridged graphs, and dual polar graphs occurring under different disguises (1skeletons, collinearity graphs, covering graphs, domains, etc.) in several seeminglyunrelated fields of mathematics: Metric graph theory; Geometric group theory; Incidence geometries and buildings; Theoretical computer science and combinatorial optimization. We give a localtoglobal characterization of weakly modular graphs and their subclasses in terms of simple connectedness of associated trianglesquare complexes and specific local combinatorial conditions. In particular, we revisit characterizations of dual polar graphs by Cameron and by BrouwerCohen. We also show that (disk)Helly graphs are precisely the cliqueHelly graphs with simply connected clique complexes. With l1embeddable weakly modular and sweakly modular graphs we associate highdimensional cell complexes, having several strong topological and geometrical properties (contractibility and the CAT([empty set]) property). Their cells have a specific structure: they are basis polyhedra of even matroids in the first case and orthoscheme complexes of gated dual polar subgraphs in the second case. We resolve some open problems concerning subclasses of weakly modular graphs: we prove a BradyMcCammond conjecture about CAT([empty set]) metric on the orthoscheme complexes of modular lattices; we answer Chastand's question about prime graphs for premedian graphs. We also explore negative curvature for weakly modular graphs"
9 editions published between 2020 and 2021 in English and held by 67 WorldCat member libraries worldwide
"This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various "nonpositive curvature" and "localto global" properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a farreaching common generalization of median graphs (and more generally, of modular and orientable modular graphs), Helly graphs, bridged graphs, and dual polar graphs occurring under different disguises (1skeletons, collinearity graphs, covering graphs, domains, etc.) in several seeminglyunrelated fields of mathematics: Metric graph theory; Geometric group theory; Incidence geometries and buildings; Theoretical computer science and combinatorial optimization. We give a localtoglobal characterization of weakly modular graphs and their subclasses in terms of simple connectedness of associated trianglesquare complexes and specific local combinatorial conditions. In particular, we revisit characterizations of dual polar graphs by Cameron and by BrouwerCohen. We also show that (disk)Helly graphs are precisely the cliqueHelly graphs with simply connected clique complexes. With l1embeddable weakly modular and sweakly modular graphs we associate highdimensional cell complexes, having several strong topological and geometrical properties (contractibility and the CAT([empty set]) property). Their cells have a specific structure: they are basis polyhedra of even matroids in the first case and orthoscheme complexes of gated dual polar subgraphs in the second case. We resolve some open problems concerning subclasses of weakly modular graphs: we prove a BradyMcCammond conjecture about CAT([empty set]) metric on the orthoscheme complexes of modular lattices; we answer Chastand's question about prime graphs for premedian graphs. We also explore negative curvature for weakly modular graphs"
Informatique mathématique : une photographie en 2019 by
Emmanuel Filiot(
Book
)
2 editions published in 2019 in French and held by 14 WorldCat member libraries worldwide
2 editions published in 2019 in French and held by 14 WorldCat member libraries worldwide
Algorithmique distribuée, calculs locaux et homomorphismes de graphes by
Jérémie Chalopin(
Book
)
2 editions published in 2006 in French and held by 2 WorldCat member libraries worldwide
Dans cette thèse, on étudie ce qui est calculable dans différents modèles d'algorithmique distribuée. Les modèles considérés correspondent à différents niveaux d'abstraction et à différents niveaux de synchronisation entre les processus d'un système distribué. On s'intéresse en particulier au problèmes de l'élection et du nommage dans ces différents modèles. Pour chaque modèle, on caractérise les systèmes distribués dans lesquels on peut résoudre ces problèmes et on étudie la complexité des problèmes de décision correspondants. Nos caractérisations utilisent des homomorphismes de graphes qui préservent certaines propriétés locales. Nos preuves sont constructives : quand on peut résoudre l'élection (ou le nommage) dans un réseau, on présente un algorithme d'élection (ou de nommage) pour ce réseau. Ces problèmes permettent de mettre en évidence les différences entre les puissances de calculs des différents modèles considérés. De plus, l'étude de ces problèmes permet de mettre à jour les bons outils qui permettent d'étudier ce qui est calculable de manière distribuée dans les différents modèles
2 editions published in 2006 in French and held by 2 WorldCat member libraries worldwide
Dans cette thèse, on étudie ce qui est calculable dans différents modèles d'algorithmique distribuée. Les modèles considérés correspondent à différents niveaux d'abstraction et à différents niveaux de synchronisation entre les processus d'un système distribué. On s'intéresse en particulier au problèmes de l'élection et du nommage dans ces différents modèles. Pour chaque modèle, on caractérise les systèmes distribués dans lesquels on peut résoudre ces problèmes et on étudie la complexité des problèmes de décision correspondants. Nos caractérisations utilisent des homomorphismes de graphes qui préservent certaines propriétés locales. Nos preuves sont constructives : quand on peut résoudre l'élection (ou le nommage) dans un réseau, on présente un algorithme d'élection (ou de nommage) pour ce réseau. Ces problèmes permettent de mettre en évidence les différences entre les puissances de calculs des différents modèles considérés. De plus, l'étude de ces problèmes permet de mettre à jour les bons outils qui permettent d'étudier ce qui est calculable de manière distribuée dans les différents modèles
On the power of synchronization between two adjacent processes by
Jérémie Chalopin(
)
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
Isometric Embedding of Busemann Surfaces into $$L_1$$ L 1 by
Jérémie Chalopin(
)
1 edition published in 2014 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2014 in English and held by 2 WorldCat member libraries worldwide
Planar Graphs Have 1string Representations by
Jérémie Chalopin(
)
1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide
Fast Approximation and Exact Computation of Negative Curvature Parameters of Graphs by
Jérémie Chalopin(
)
1 edition published in 2019 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2019 in English and held by 2 WorldCat member libraries worldwide
Election in partially anonymous networks with arbitrary knowledge in message passing systems by
Jérémie Chalopin(
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
Rendezvous in networks in spite of delay faults by
Jérémie Chalopin(
)
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
Cubes partiels : complétion, compression, plongement by
Manon Philibert(
)
1 edition published in 2021 in French and held by 1 WorldCat member library worldwide
Partial cubes (aka isometric subgraphs of hypercubes) are a fundamental class of metric graph theory. They comprise many important graph classes (trees, median graphs, tope graphs of complexes of oriented matroids, etc.), arising from different areas of research such as discrete geometry, combinatorics or geometric group theory.First, we investigate the structure of partial cubes of VCdimension 2. We show that those graphs can be obtained via amalgams from even cycles and full subdivisions of complete graphs. This decomposition allows us to obtain various characterizations. In particular, any partial cube can be completed to an ample partial cube of VCdimension 2. Then, we show that the tope graphs of oriented matroids and complexes of uniform oriented matroids can also be completed to ample partial cubes of the same VCdimension.Using a result of Moran and Warmuth, we establish that those classes satisfy the conjecture of Floyd and Warmuth, one of the oldest open problems in computational machine learning. Particularly, they admit (improper labeled) compression schemes of size their VCdimension.Next, we describe a proper labeled compression scheme of size d for complexes of oriented matroids of VCdimension d, generalizing the result of Moran and Warmuth for ample sets. Finally, we give a characterization via excluded pcminors and via forbidden isometric subgraphs of partial cubes isometrically embedded into the grid mathbb{Z}^2 and the cylinder P_n square C_{2k} for some n and k > 4
1 edition published in 2021 in French and held by 1 WorldCat member library worldwide
Partial cubes (aka isometric subgraphs of hypercubes) are a fundamental class of metric graph theory. They comprise many important graph classes (trees, median graphs, tope graphs of complexes of oriented matroids, etc.), arising from different areas of research such as discrete geometry, combinatorics or geometric group theory.First, we investigate the structure of partial cubes of VCdimension 2. We show that those graphs can be obtained via amalgams from even cycles and full subdivisions of complete graphs. This decomposition allows us to obtain various characterizations. In particular, any partial cube can be completed to an ample partial cube of VCdimension 2. Then, we show that the tope graphs of oriented matroids and complexes of uniform oriented matroids can also be completed to ample partial cubes of the same VCdimension.Using a result of Moran and Warmuth, we establish that those classes satisfy the conjecture of Floyd and Warmuth, one of the oldest open problems in computational machine learning. Particularly, they admit (improper labeled) compression schemes of size their VCdimension.Next, we describe a proper labeled compression scheme of size d for complexes of oriented matroids of VCdimension d, generalizing the result of Moran and Warmuth for ample sets. Finally, we give a characterization via excluded pcminors and via forbidden isometric subgraphs of partial cubes isometrically embedded into the grid mathbb{Z}^2 and the cylinder P_n square C_{2k} for some n and k > 4
Local certification in distributed computing : errorsensitivity, uniformity, redundancy, and interactivity by
Laurent Feuilloley(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
This dissertation is about local certification, a central topic in distributed decision, a subfield of distributed computing. The distributed decision mechanism consists, for the nodes of a network, in deciding in a distributed manner whether the network is in a proper configuration or not, with respect to some fixed predicate. This decision is said to be local because the nodes of the network can communicate only with their neighbours. After communication, every node outputs a decision, stating whether the network is locally correct, that is, correct given the partial information gathered so far by this node. The network is declared to be globally correct, if and only if, it is declared to be locally correct by every node.Most predicates cannot be verified by this type of computation, due to the locality constraint. Local certification is a mechanism that enables to circumvent this difficulty, and to check any property. It consists in providing the nodes of the network with labels, called certificates, that can be verified locally by a distributed algorithm. A local certification scheme is correct if only the networks that satisfy the predicate can be certified. In addition to its theoretical appeal, as a form of distributed nondeterminism, the concept of local certification is especially relevant in the study of faulttolerant distributed algorithms, where a key step consists in checking the status of the network, based on information stored at the nodes.This dissertation deals with four aspects of local certification: errorsensitivity, uniformity, redundancy, and interactivity. The study of these four topics is motivated by the same essential question: How to reduce the resources needed for certification, and/or ensure a better faulttolerance? In order to tackle this question we have to understand fundamental properties of certification. In particular, in this dissertation we answer questions such as: How redundant the certificates need to be for a proper certification? Are the classic certification protocols robust to a strengthening of the acceptance condition? and, How does introducing interactivity in the process changes the complexity of certification?
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
This dissertation is about local certification, a central topic in distributed decision, a subfield of distributed computing. The distributed decision mechanism consists, for the nodes of a network, in deciding in a distributed manner whether the network is in a proper configuration or not, with respect to some fixed predicate. This decision is said to be local because the nodes of the network can communicate only with their neighbours. After communication, every node outputs a decision, stating whether the network is locally correct, that is, correct given the partial information gathered so far by this node. The network is declared to be globally correct, if and only if, it is declared to be locally correct by every node.Most predicates cannot be verified by this type of computation, due to the locality constraint. Local certification is a mechanism that enables to circumvent this difficulty, and to check any property. It consists in providing the nodes of the network with labels, called certificates, that can be verified locally by a distributed algorithm. A local certification scheme is correct if only the networks that satisfy the predicate can be certified. In addition to its theoretical appeal, as a form of distributed nondeterminism, the concept of local certification is especially relevant in the study of faulttolerant distributed algorithms, where a key step consists in checking the status of the network, based on information stored at the nodes.This dissertation deals with four aspects of local certification: errorsensitivity, uniformity, redundancy, and interactivity. The study of these four topics is motivated by the same essential question: How to reduce the resources needed for certification, and/or ensure a better faulttolerance? In order to tackle this question we have to understand fundamental properties of certification. In particular, in this dissertation we answer questions such as: How redundant the certificates need to be for a proper certification? Are the classic certification protocols robust to a strengthening of the acceptance condition? and, How does introducing interactivity in the process changes the complexity of certification?
Analyses et preuves formelles d'algorithmes distribués probabilistes by
Allyx Fontaine(
)
1 edition published in 2014 in French and held by 1 WorldCat member library worldwide
Probabilistic algorithms are simple to formulate. However, theiranalysis can become very complex, especially in the field of distributedcomputing. We present algorithms  optimal in terms of bit complexityand solving the problems of MIS and maximal matching in rings  that followthe same scheme.We develop a method that unifies the bit complexitylower bound results to solve MIS, maximal matching and coloration problems.The complexity of these analyses, which can easily lead to errors,together with the existence of many models depending on implicit assumptionsmotivated us to formally model the probabilistic distributed algorithmscorresponding to our model (message passing, anonymous andsynchronous). Our aim is to formally prove the properties related to theiranalysis. For this purpose, we develop a library, called RDA, based on theCoq proof assistant
1 edition published in 2014 in French and held by 1 WorldCat member library worldwide
Probabilistic algorithms are simple to formulate. However, theiranalysis can become very complex, especially in the field of distributedcomputing. We present algorithms  optimal in terms of bit complexityand solving the problems of MIS and maximal matching in rings  that followthe same scheme.We develop a method that unifies the bit complexitylower bound results to solve MIS, maximal matching and coloration problems.The complexity of these analyses, which can easily lead to errors,together with the existence of many models depending on implicit assumptionsmotivated us to formally model the probabilistic distributed algorithmscorresponding to our model (message passing, anonymous andsynchronous). Our aim is to formally prove the properties related to theiranalysis. For this purpose, we develop a library, called RDA, based on theCoq proof assistant
Impact des connaissances initiales sur la calculabilité distribuée by
Antoine Naudin(
)
1 edition published in 2017 in French and held by 1 WorldCat member library worldwide
In this study, we show how knowledge impacts the computability in distributed systems. First, we characterize what we need to know to elect in the unknown participant model. This model is a natural extension for the message passing model that formalises dynamicity that occurs in some networks. We give a necessary and sufficient condition on the knowledge needed to solve the following fundamental problems : map construction, leader election and kleader election. For each of them, we provide an algorithm solving the problem using any knowledge satisfying our condition. Then, we extend the model to anonymous networks. We characterize, with the same methodology, the knowledge needed to solve an election in this model and we provide an algorithm using such a knowledge and a bound on the size of the network. In the second part, we study the impact of local knowledge on the computability of the anonymous graph exploration problem. We introduce a new model of mobile agents where an agent is endowed with binoculars, a local sensor permitting to perceive the graph induced by the vertices adjacent to its location. In this model, we characterize the graphs that can be explored by a single mobile agent without any global information and we provide an algorithm exploring all of them. Unfortunately, universal algorithm has a cost : The number of moves required by such an algorithm cannot be bounded by a computable function. Finally, we prove that large classes of graphs like chordal graphs, Johnson graphs, . . . can be explored in a linear number of moves using binoculars by providing an exploration algorithm for the family of Weetman graphs
1 edition published in 2017 in French and held by 1 WorldCat member library worldwide
In this study, we show how knowledge impacts the computability in distributed systems. First, we characterize what we need to know to elect in the unknown participant model. This model is a natural extension for the message passing model that formalises dynamicity that occurs in some networks. We give a necessary and sufficient condition on the knowledge needed to solve the following fundamental problems : map construction, leader election and kleader election. For each of them, we provide an algorithm solving the problem using any knowledge satisfying our condition. Then, we extend the model to anonymous networks. We characterize, with the same methodology, the knowledge needed to solve an election in this model and we provide an algorithm using such a knowledge and a bound on the size of the network. In the second part, we study the impact of local knowledge on the computability of the anonymous graph exploration problem. We introduce a new model of mobile agents where an agent is endowed with binoculars, a local sensor permitting to perceive the graph induced by the vertices adjacent to its location. In this model, we characterize the graphs that can be explored by a single mobile agent without any global information and we provide an algorithm exploring all of them. Unfortunately, universal algorithm has a cost : The number of moves required by such an algorithm cannot be bounded by a computable function. Finally, we prove that large classes of graphs like chordal graphs, Johnson graphs, . . . can be explored in a linear number of moves using binoculars by providing an exploration algorithm for the family of Weetman graphs
Accords exacts et approchés pour les adversaires de message by Eloi Perdereau(
)
1 edition published in 2021 in French and held by 1 WorldCat member library worldwide
Our subject is about computability of distributed systems in the messageadversaries family of models.For this purpose, several mathematical approaches are carried out.For instance, based on recent advances in the subject, we use well knowntopological methods to solve our problems.But we also used geometric, combinatorial and dynamical systems methods.In the first part, we are interested in the Consensus problem and the kSetAgreement.They are what we called exact agreements, i.e. the decision values must beamong the proposed ones.As a complement to FG11, we have characterized topologically the solvability ofthe Binary Consensus problem with two process in the general model of messageadversaries.This new characterization gives a better intuition of the result.We also characterized the solvability of kSet Agreement in omissionadversaries by giving the number of omission faults a system can tolerate inorder to solve the problem on an underlying communication graph.Doing so, we based our result on a topological method that we extended to ourgraphical models.Finally, we studied in a second part some approximate variations of the kSetAgreement problem.In this approximate setting, the decision values are required to be close toone another, based on some precise conditions.Several variations were studied, most notably an asymptotic version thatdoesn't requires processes to explicitly terminatebut rather requires a certain type of convergence of the values.Theses results shows the diversity and intricacy of the questions that are atstake
1 edition published in 2021 in French and held by 1 WorldCat member library worldwide
Our subject is about computability of distributed systems in the messageadversaries family of models.For this purpose, several mathematical approaches are carried out.For instance, based on recent advances in the subject, we use well knowntopological methods to solve our problems.But we also used geometric, combinatorial and dynamical systems methods.In the first part, we are interested in the Consensus problem and the kSetAgreement.They are what we called exact agreements, i.e. the decision values must beamong the proposed ones.As a complement to FG11, we have characterized topologically the solvability ofthe Binary Consensus problem with two process in the general model of messageadversaries.This new characterization gives a better intuition of the result.We also characterized the solvability of kSet Agreement in omissionadversaries by giving the number of omission faults a system can tolerate inorder to solve the problem on an underlying communication graph.Doing so, we based our result on a topological method that we extended to ourgraphical models.Finally, we studied in a second part some approximate variations of the kSetAgreement problem.In this approximate setting, the decision values are required to be close toone another, based on some precise conditions.Several variations were studied, most notably an asymptotic version thatdoesn't requires processes to explicitly terminatebut rather requires a certain type of convergence of the values.Theses results shows the diversity and intricacy of the questions that are atstake
Présentation et étude de quelques problèmes d'algorithmique distribuée by
Thomas Morsellino(
)
1 edition published in 2012 in French and held by 1 WorldCat member library worldwide
Nous proposons tout d'abord une étude de plusieurs problèmes de l'algorithmique distribuée. Nous fournissons un modèle formel appliqué aux réseaux de diffusion anonymes. Dans ce modèle, nous caractérisons les graphes dans lesquels il est possible de résoudre l'énumération et l'élection. Cette caractérisation se base sur la notion d'homomorphisme de graphes. Nous proposons deux algorithmes dont la complexité est polynomiale et qui améliorent les complexités exponentielles connues jusqu'à présent. Dans un second temps, nous étudions le problème du calcul de l'état global et nous introduisons la notion de weak snapshot. Nous montrons qu'il existe des solutions pour ce problème dans les réseaux anonymes. Nous présentons plusieurs résultats concernant le calcul de l'état global en liaison avec des applications telles que le calcul de points de reprise, la détection de la terminaison ou encore le calcul d'une cartographie du réseau. Dans un cadre plus pratique, nous présentons la conception, le développement et l'implémentation des algorithmes proposés pour le calcul de l'état global au sein du logiciel de simulation et de visualisation ViSiDiA
1 edition published in 2012 in French and held by 1 WorldCat member library worldwide
Nous proposons tout d'abord une étude de plusieurs problèmes de l'algorithmique distribuée. Nous fournissons un modèle formel appliqué aux réseaux de diffusion anonymes. Dans ce modèle, nous caractérisons les graphes dans lesquels il est possible de résoudre l'énumération et l'élection. Cette caractérisation se base sur la notion d'homomorphisme de graphes. Nous proposons deux algorithmes dont la complexité est polynomiale et qui améliorent les complexités exponentielles connues jusqu'à présent. Dans un second temps, nous étudions le problème du calcul de l'état global et nous introduisons la notion de weak snapshot. Nous montrons qu'il existe des solutions pour ce problème dans les réseaux anonymes. Nous présentons plusieurs résultats concernant le calcul de l'état global en liaison avec des applications telles que le calcul de points de reprise, la détection de la terminaison ou encore le calcul d'une cartographie du réseau. Dans un cadre plus pratique, nous présentons la conception, le développement et l'implémentation des algorithmes proposés pour le calcul de l'état global au sein du logiciel de simulation et de visualisation ViSiDiA
ALGOTEL 2009 : actes de la conférence : CarryleRouet 1619 juin 2009 by Rencontres Francophones sur les Aspects Algoithmiques des Télécommunications(
Book
)
1 edition published in 2009 in French and held by 1 WorldCat member library worldwide
1 edition published in 2009 in French and held by 1 WorldCat member library worldwide
How simple robots benefit from looking back : reconstructing visibility graphs of polygons(
)
1 edition published in 2010 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2010 in English and held by 0 WorldCat member libraries worldwide
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Associated Subjects