Thomassé, Stéphan
Overview
Works:  27 works in 32 publications in 2 languages and 44 library holdings 

Roles:  Opponent, Thesis advisor, Author, Other, Editor 
Publication Timeline
.
Most widely held works by
Stéphan Thomassé
Grundy sets of partial orders by
W Deuber(
Book
)
1 edition published in 1996 in English and held by 10 WorldCat member libraries worldwide
1 edition published in 1996 in English and held by 10 WorldCat member libraries worldwide
Decompositions and orientations of hypergraphs by
Jørgen BangJensen(
Book
)
3 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
Categoricite, belordre et decomposabilite des relations by
Stéphan Thomassé(
Book
)
2 editions published in 1995 in French and held by 2 WorldCat member libraries worldwide
CETTE THESE PRESENTE DIFFERENTS ASPECTS DE L'ABRITEMENT ENTRE RELATIONS. LORSQUE R EST UNE RELATION DENOMBRABLE, NOUS Y PROUVONS (ET CE FIL CONDUCTEUR TRAVERSE LES DIFFERENTES NOTIONS ABORDEES) LA CHAINE D'IMPLICATIONS SUIVANTE: LES INDECOMPOSABLES ABRITES DANS R SONT DE TAILLE AU PLUS N (2 POUR LES SERIE PARALLELE OU LES CHAINES). LA CLASSE DES COLORATIONS DE R EN TROIS COULEURS EST BELORDONNEE PAR ABRITEMENT (LAVER LE PROUVE POUR LES CHAINES ET COROMINAS POUR LES ARBRES.) L'ENSEMBLE DES PARTIES DE R QUI ABRITENT R EST COMAIGRE. L'ENSEMBLE DES PARTIES DE R QUI ABRITENT R EST DE MESURE NON NULLE. CES PROPRIETES SONT ORDONNEES DE LA PLUS FORTE A LA PLUS FAIBLE ET NE SONT PAS EQUIVALENTES. TOUTEFOIS, ET C'EST L'OBJET DU DERNIER CHAPITRE, CES DIFFERENTES NOTIONS SE BASENT SUR LES EXTENSIONS FINIES D'ISOMORPHISMES LOCAUX. EN EFFET, ETIQUETER UN GRAPHE EN 2 COULEURS PEUT REPRESENTER L'AJOUT D'UN SOMMET, TOUT INDECOMPOSABLE INCLUS DANS UN AUTRE INDECOMPOSABLE PEUT S'ETENDRE A TOUTE PARTIE FINIE EN UN INDECOMPOSABLE (ILLE), ET ENFIN LES PREUVES DE CATEGORICITE ET DE MESURABILITE SE BASENT SUR L'OPERATION A DE LUSIN APPLIQUEE A L'ARBRE DES ISOMORPHISMES LOCAUX. LA NOTION D'ALPHAMORPHISME DE FRAISSE POURRAIT PERMETTRE DE TRADUIRE CES DIFFERENTES PROPRIETES. DANS CETTE OPTIQUE, NOUS MONTRONS UNE FACON DE L'UTILISER POUR PROUVER LE THEOREME D'IMPARTIABILITE DE POUZET QUI JUSQU'ALORS NECESSITAIT L'EMPLOI DE RESULTATS TOPOLOGIQUES
2 editions published in 1995 in French and held by 2 WorldCat member libraries worldwide
CETTE THESE PRESENTE DIFFERENTS ASPECTS DE L'ABRITEMENT ENTRE RELATIONS. LORSQUE R EST UNE RELATION DENOMBRABLE, NOUS Y PROUVONS (ET CE FIL CONDUCTEUR TRAVERSE LES DIFFERENTES NOTIONS ABORDEES) LA CHAINE D'IMPLICATIONS SUIVANTE: LES INDECOMPOSABLES ABRITES DANS R SONT DE TAILLE AU PLUS N (2 POUR LES SERIE PARALLELE OU LES CHAINES). LA CLASSE DES COLORATIONS DE R EN TROIS COULEURS EST BELORDONNEE PAR ABRITEMENT (LAVER LE PROUVE POUR LES CHAINES ET COROMINAS POUR LES ARBRES.) L'ENSEMBLE DES PARTIES DE R QUI ABRITENT R EST COMAIGRE. L'ENSEMBLE DES PARTIES DE R QUI ABRITENT R EST DE MESURE NON NULLE. CES PROPRIETES SONT ORDONNEES DE LA PLUS FORTE A LA PLUS FAIBLE ET NE SONT PAS EQUIVALENTES. TOUTEFOIS, ET C'EST L'OBJET DU DERNIER CHAPITRE, CES DIFFERENTES NOTIONS SE BASENT SUR LES EXTENSIONS FINIES D'ISOMORPHISMES LOCAUX. EN EFFET, ETIQUETER UN GRAPHE EN 2 COULEURS PEUT REPRESENTER L'AJOUT D'UN SOMMET, TOUT INDECOMPOSABLE INCLUS DANS UN AUTRE INDECOMPOSABLE PEUT S'ETENDRE A TOUTE PARTIE FINIE EN UN INDECOMPOSABLE (ILLE), ET ENFIN LES PREUVES DE CATEGORICITE ET DE MESURABILITE SE BASENT SUR L'OPERATION A DE LUSIN APPLIQUEE A L'ARBRE DES ISOMORPHISMES LOCAUX. LA NOTION D'ALPHAMORPHISME DE FRAISSE POURRAIT PERMETTRE DE TRADUIRE CES DIFFERENTES PROPRIETES. DANS CETTE OPTIQUE, NOUS MONTRONS UNE FACON DE L'UTILISER POUR PROUVER LE THEOREME D'IMPARTIABILITE DE POUZET QUI JUSQU'ALORS NECESSITAIT L'EMPLOI DE RESULTATS TOPOLOGIQUES
Stabilité et décomposition en circuits d'un digraphe by
Stéphane Bessy(
Book
)
2 editions published in 2003 in French and held by 2 WorldCat member libraries worldwide
En 1963, T. Gallai conjectura que les sommets de tout digraphe fortement connexe D peuvent être couverts par au plus alpha(D) circuits, où alpha(D) désigne la stabilité de D. Cette thèse présente une preuve de cette conjecture obtenue conjointement avec S. Thomassé et pour laquelle de nouvelles structures combinatoires sont introduites: les ordres cycliques pour digraphes fortement connexes. Un second résultat est présenté: pour un digraphe fortement connexe D, il existe au plus 2.alpha(D)1 circuits couvrant le digraphe D et dont l'union est fortement connexe et possède au plus D+2.alpha(D)2 arcs. De ce résultat dérive un algorithme d'approximation polynomial pour trouver le sous digraphe couvrant fortement connexe de D ayant un nombre minimal d'arcs. L'aspect algorithmique des décompositions est traité. De plus, deux conjectures sont étudiées sur le rôle que la connectivité du digraphe D pourrait jouer dans l'existence de différentes décompositions en chemins ou circuits
2 editions published in 2003 in French and held by 2 WorldCat member libraries worldwide
En 1963, T. Gallai conjectura que les sommets de tout digraphe fortement connexe D peuvent être couverts par au plus alpha(D) circuits, où alpha(D) désigne la stabilité de D. Cette thèse présente une preuve de cette conjecture obtenue conjointement avec S. Thomassé et pour laquelle de nouvelles structures combinatoires sont introduites: les ordres cycliques pour digraphes fortement connexes. Un second résultat est présenté: pour un digraphe fortement connexe D, il existe au plus 2.alpha(D)1 circuits couvrant le digraphe D et dont l'union est fortement connexe et possède au plus D+2.alpha(D)2 arcs. De ce résultat dérive un algorithme d'approximation polynomial pour trouver le sous digraphe couvrant fortement connexe de D ayant un nombre minimal d'arcs. L'aspect algorithmique des décompositions est traité. De plus, deux conjectures sont étudiées sur le rôle que la connectivité du digraphe D pourrait jouer dans l'existence de différentes décompositions en chemins ou circuits
A Polynomial TuringKernel for Weighted Independent Set in BullFree Graphs by
Stéphan Thomassé(
)
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
Topologie et algorithmes sur les cartes combinatoires by
Vincent Despré(
)
1 edition published in 2016 in French and held by 2 WorldCat member libraries worldwide
Dans cette thèse, nous nous intéressons aux propriétés topologiques des surfaces, i.e. celles qui sont préservées par des déformations continues. Intuitivement, ces propriétés peuvent être imaginées comme étant celles qui décrivent le forme générale des surfaces. Nous utilisons des cartes combinatoires pour décrire les surfaces. Elles ont le double avantage d'être de naturels objets mathématiques et de pouvoir être transformées naturellement en structure de données.Nous étudions trois problèmes différents. Premièrement, nous donnons des algorithmes pour calculer le nombre géométrique d'intersection de courbes dessinées sur des surfaces. Nous avons obtenu un algorithm quadratique pour calculer le nombre minimal d'autointersections dans une classe d'homotopie, un algorithme quartique pour construire un représentant minimal et un algorithme quasilinéaire pour décider si une classe d'homotopie contient une courbe simple. Ensuite, nous donnons des contreexemples à une conjecture de Mohar et Thomassen au sujet de l'existence de cycles de partage dans les triangulations. Finalement, nous utilisons les travaux récents de Lévèque et Gonçalves à propos des bois de Schnyder toriques pour construire une bijection entre les triangulations du tore et certaines cartes unicellulaires analogue à le célèbre bijection de Poulalhon et Schaeffer pour les triangulations planaires.Plusieurs points de vue sont utilisés au cours de cette thèse. Nous proposons donc un important chapitre préliminaire où nous insistons sur les connections entre ces différents points de vue
1 edition published in 2016 in French and held by 2 WorldCat member libraries worldwide
Dans cette thèse, nous nous intéressons aux propriétés topologiques des surfaces, i.e. celles qui sont préservées par des déformations continues. Intuitivement, ces propriétés peuvent être imaginées comme étant celles qui décrivent le forme générale des surfaces. Nous utilisons des cartes combinatoires pour décrire les surfaces. Elles ont le double avantage d'être de naturels objets mathématiques et de pouvoir être transformées naturellement en structure de données.Nous étudions trois problèmes différents. Premièrement, nous donnons des algorithmes pour calculer le nombre géométrique d'intersection de courbes dessinées sur des surfaces. Nous avons obtenu un algorithm quadratique pour calculer le nombre minimal d'autointersections dans une classe d'homotopie, un algorithme quartique pour construire un représentant minimal et un algorithme quasilinéaire pour décider si une classe d'homotopie contient une courbe simple. Ensuite, nous donnons des contreexemples à une conjecture de Mohar et Thomassen au sujet de l'existence de cycles de partage dans les triangulations. Finalement, nous utilisons les travaux récents de Lévèque et Gonçalves à propos des bois de Schnyder toriques pour construire une bijection entre les triangulations du tore et certaines cartes unicellulaires analogue à le célèbre bijection de Poulalhon et Schaeffer pour les triangulations planaires.Plusieurs points de vue sont utilisés au cours de cette thèse. Nous proposons donc un important chapitre préliminaire où nous insistons sur les connections entre ces différents points de vue
Parameterized Domination in Circle Graphs by Nicolas Bousquet(
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
EdgePartitioning a Graph into Paths: Beyond the BarátThomassen Conjecture by
Julien Bensmail(
)
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
WellQuasiOrder of Relabel Functions by
Jean Daligault(
)
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
Coloring Dense Digraphs by Ararat Harutyunyan(
)
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
Trigraphes de Berge apprivoisés by
Théophile Trunck(
)
1 edition published in 2014 in French and held by 1 WorldCat member library worldwide
The goal of this these is to use graph's decompositions to solve algorithmic problems on graphs. We will study the class of Berge tame graphs. A Berge graph is a graph without cycle of odd length at least 4 nor complement of cycle of odd length at least 4.In the 60's, Claude Berge conjectured that Berge graphs are perfect graphs. The size of the biggest clique is exactly the number of colors required to color the graph. In 2002, Chudnovsky, Robertson, Seymour et Thomas proved this conjecture using a theorem of decomposition: Berge graphs are either basic or have a decomposition. This is a useful result to do proof by induction. Unfortunately, one of the decomposition, the skewpartition, is really hard to use. We arefocusing here on Berge tame graphs, i.e~Berge graph without balanced skewpartition. To be able to do induction, we must first adapt the Chudnovsky et al's theorem of structure to our class. We prove a stronger result: Berge tame graphs are basic or have a decomposition such that one side is always basic. We also have an algorithm to compute this decomposition. We then use our theorem to prouve that Berge tame graphs have the bigbipartite property, the cliquestable set separation property and there exists a polytime algorithm to compute the maximum stable set
1 edition published in 2014 in French and held by 1 WorldCat member library worldwide
The goal of this these is to use graph's decompositions to solve algorithmic problems on graphs. We will study the class of Berge tame graphs. A Berge graph is a graph without cycle of odd length at least 4 nor complement of cycle of odd length at least 4.In the 60's, Claude Berge conjectured that Berge graphs are perfect graphs. The size of the biggest clique is exactly the number of colors required to color the graph. In 2002, Chudnovsky, Robertson, Seymour et Thomas proved this conjecture using a theorem of decomposition: Berge graphs are either basic or have a decomposition. This is a useful result to do proof by induction. Unfortunately, one of the decomposition, the skewpartition, is really hard to use. We arefocusing here on Berge tame graphs, i.e~Berge graph without balanced skewpartition. To be able to do induction, we must first adapt the Chudnovsky et al's theorem of structure to our class. We prove a stronger result: Berge tame graphs are basic or have a decomposition such that one side is always basic. We also have an algorithm to compute this decomposition. We then use our theorem to prouve that Berge tame graphs have the bigbipartite property, the cliquestable set separation property and there exists a polytime algorithm to compute the maximum stable set
Detection of linear algebra operations in polyhedral programs by
Guillaume Iooss(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Writing a code which uses an architecture at its full capability has become an increasingly difficult problem over the last years. For some key operations, a dedicated accelerator or a finely tuned implementation exists and delivers the best performance. Thus, when compiling a code, identifying these operations and issuing calls to their highperformance implementation is attractive. In this dissertation, we focus on the problem of detection of these operations. We propose a framework which detects linear algebra subcomputations within a polyhedral program. The main idea of this framework is to partition the computation in order to isolate different subcomputations in a regular manner, then we consider each portion of the computation and try to recognize it as a combination of linear algebra operations.We perform the partitioning of the computation by using a program transformation called monoparametric tiling. This transformation partitions the computation into blocks, whose shape is some homothetic scaling of a fixedsize partitioning. We show that the tiled program remains polyhedral while allowing a limited amount of parametrization: a single size parameter. This is an improvement compared to the previous work on tiling, that forced us to choose between these two properties.Then, in order to recognize computations, we introduce a template recognition algorithm. This template recognition algorithm is built on a stateoftheart program equivalence algorithm. We also propose several extensions in order to manage some semantic properties.Finally, we combine these two previous contributions into a framework which detects linear algebra subcomputations. A part of this framework is a library of template, based on the BLAS specification. We demonstrate our framework on several applications
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Writing a code which uses an architecture at its full capability has become an increasingly difficult problem over the last years. For some key operations, a dedicated accelerator or a finely tuned implementation exists and delivers the best performance. Thus, when compiling a code, identifying these operations and issuing calls to their highperformance implementation is attractive. In this dissertation, we focus on the problem of detection of these operations. We propose a framework which detects linear algebra subcomputations within a polyhedral program. The main idea of this framework is to partition the computation in order to isolate different subcomputations in a regular manner, then we consider each portion of the computation and try to recognize it as a combination of linear algebra operations.We perform the partitioning of the computation by using a program transformation called monoparametric tiling. This transformation partitions the computation into blocks, whose shape is some homothetic scaling of a fixedsize partitioning. We show that the tiled program remains polyhedral while allowing a limited amount of parametrization: a single size parameter. This is an improvement compared to the previous work on tiling, that forced us to choose between these two properties.Then, in order to recognize computations, we introduce a template recognition algorithm. This template recognition algorithm is built on a stateoftheart program equivalence algorithm. We also propose several extensions in order to manage some semantic properties.Finally, we combine these two previous contributions into a framework which detects linear algebra subcomputations. A part of this framework is a library of template, based on the BLAS specification. We demonstrate our framework on several applications
Problèmes de connexité en théorie de graphes : structures, algorithmes et complexité by
Florian Hoersch(
)
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
This thesis is concerned with 3 classes of problems related to graph theory. Firstly, we deal with graph orientations where an orientation of a graph is obtained by replacing every edge by an arc between the same two vertices. This section is divided into two parts, one on orientations for edgeconnectivity and one on orientations for vertexconnectivity. For edgeconnectivity, we first review some results related to the strong orientation theorem of NashWilliams and show that it is coNPhard to decide whether a given oddvertex pairing is admissible. We next show that it is NPhard to decide whether a given graph has an orientation satisfying some arbitrary local edgeconnectivity condition and give some related problems. We then give some partial results on the problem of determining whether a given graph has a strongly connected orientation such that the indegree of every vertex is of a prescribed parity. Finally, we deal with an orientation property of 3edgeconnected graphs that is located between strong connectivity and 2arcconnectivity. For vertexconnectivity, we first give an overview of previous results and then determine some more restricted classes of eulerian graphs all of whose eulerian orientations are highly vertexconnected. Next, we deal with arborescence packings. We first give a construction that allows to derive theorems on packings of reachability arborescences from theorems on packings of spanning arborescences in several settings. In particular, we conclude a thorem of Kamiyama, Katoh and Takizawa from a strong form of the theorem of Edmonds. We next use matroid intersection to obtain a theorem on packing mixed hyperarborescences in a setting where the roots of the arborescences are not fixed. Finally, we provide FPT algorithms for a problem on packing arborescences and some similar objects that have to satisfy a little extra condition. In the last part, we deal with connectivity augmentation problems. In particular, relying on some structure provided by Durand de Gevigney and Szigeti, we give a fast algorithm for (2,k)connectivity augmentation
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
This thesis is concerned with 3 classes of problems related to graph theory. Firstly, we deal with graph orientations where an orientation of a graph is obtained by replacing every edge by an arc between the same two vertices. This section is divided into two parts, one on orientations for edgeconnectivity and one on orientations for vertexconnectivity. For edgeconnectivity, we first review some results related to the strong orientation theorem of NashWilliams and show that it is coNPhard to decide whether a given oddvertex pairing is admissible. We next show that it is NPhard to decide whether a given graph has an orientation satisfying some arbitrary local edgeconnectivity condition and give some related problems. We then give some partial results on the problem of determining whether a given graph has a strongly connected orientation such that the indegree of every vertex is of a prescribed parity. Finally, we deal with an orientation property of 3edgeconnected graphs that is located between strong connectivity and 2arcconnectivity. For vertexconnectivity, we first give an overview of previous results and then determine some more restricted classes of eulerian graphs all of whose eulerian orientations are highly vertexconnected. Next, we deal with arborescence packings. We first give a construction that allows to derive theorems on packings of reachability arborescences from theorems on packings of spanning arborescences in several settings. In particular, we conclude a thorem of Kamiyama, Katoh and Takizawa from a strong form of the theorem of Edmonds. We next use matroid intersection to obtain a theorem on packing mixed hyperarborescences in a setting where the roots of the arborescences are not fixed. Finally, we provide FPT algorithms for a problem on packing arborescences and some similar objects that have to satisfy a little extra condition. In the last part, we deal with connectivity augmentation problems. In particular, relying on some structure provided by Durand de Gevigney and Szigeti, we give a fast algorithm for (2,k)connectivity augmentation
Shift spaces on groups : computability and dynamics by
Sebastián Andrés Barbieri Lemp(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Shift spaces are sets of colorings of a group which avoid a set of forbidden patterns and are endowed with a shift action. These spaces appear naturally as discrete versions of dynamical systems: they are obtained by partitioning the phase space and mapping each element into the sequence of partitions visited by its orbit.Severa! breakthroughs in this domain have pointed out the intricate relationship between dynamics of shift spaces and their computability properties. One remarkable example is the classification of the entropies of multidimensional subshifts of finite type as the set of right recursively enumerable numbers. This work explores shift spaces with a dual approach: on the one hand we are interested in their dynamical properties and on the ether hand we studythese abjects as computational models.Four salient results have been obtained as a result of this approach: (1) a combinatorial condition ensuring nonemptiness of subshifts on arbitrary countable groups; (2) a simulation theorem which realizes effective actions of finitely generated groups as factors of a subaction of a subshift of finite type; (3) a characterization of effectiveness with oracles using generalized Turing machines and (4) the undecidability of the torsion problem for two group invariants of shift spaces.As byproducts of these results we obtain a simple proof of the existence of strongly aperiodic subshifts in countable groups. Furthermore, we realize them as subshifts of finite type in the case of a semidirect product of a ddimensional integer lattice with a finitely generated group with decida ble word problem whenever d> 1
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Shift spaces are sets of colorings of a group which avoid a set of forbidden patterns and are endowed with a shift action. These spaces appear naturally as discrete versions of dynamical systems: they are obtained by partitioning the phase space and mapping each element into the sequence of partitions visited by its orbit.Severa! breakthroughs in this domain have pointed out the intricate relationship between dynamics of shift spaces and their computability properties. One remarkable example is the classification of the entropies of multidimensional subshifts of finite type as the set of right recursively enumerable numbers. This work explores shift spaces with a dual approach: on the one hand we are interested in their dynamical properties and on the ether hand we studythese abjects as computational models.Four salient results have been obtained as a result of this approach: (1) a combinatorial condition ensuring nonemptiness of subshifts on arbitrary countable groups; (2) a simulation theorem which realizes effective actions of finitely generated groups as factors of a subaction of a subshift of finite type; (3) a characterization of effectiveness with oracles using generalized Turing machines and (4) the undecidability of the torsion problem for two group invariants of shift spaces.As byproducts of these results we obtain a simple proof of the existence of strongly aperiodic subshifts in countable groups. Furthermore, we realize them as subshifts of finite type in the case of a semidirect product of a ddimensional integer lattice with a finitely generated group with decida ble word problem whenever d> 1
Patterns in Large Graphs by
Tien Nam Le(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Un graphe est un ensemble de noeuds, ensemble de liens reliant des paires de noeuds. Avec la quantité accumulée de données collectées, il existe un intérêt croissant pour la compréhension des structures et du comportement de très grands graphes. Néanmoins, l'augmentation rapide de la taille des grands graphes rend l'étude de tous les graphes de moins en moins efficace. Ainsi, il existe une demande impérieuse pour des méthodes plus efficaces pour étudier de grands graphes sans nécessiter la connaissance de tous les graphes. Une méthode prometteuse pour comprendre le comportement de grands graphes consiste à exploiter des propriétés spécifiques de structures locales, telles que la taille des grappes ou la présence locale d'un motif spécifique, c'estàdire un graphe donné (généralement petit). Un exemple classique de la théorie des graphes (cas avérés de la conjecture d'ErdosHajnal) est que, si un graphe de grande taille ne contient pas de motif spécifique, il doit alors avoir un ensemble de noeuds liés par paires ou non liés, de taille exponentiellement plus grande que prévue. Cette thèse abordera certains aspects de deux questions fondamentales de la théorie des graphes concernant la présence, en abondance ou à peine, d'un motif donné dans un grand graphe :  Le grand graphe peutil être partitionné en copies du motif ?  Le grand graphe contientil une copie du motif ? Nous discuterons de certaines des conjectures les plus connues de la théorie des graphes sur ce sujet: les conjectures de Tutte sur les flots dans les graphes et la conjecture d'ErdosHajnal mentionnée cidessus, et présenterons des preuves pour plusieurs conjectures connexes  y compris la conjecture de BarátThomassen, une conjecture de Haggkvist et Krissell, un cas particulier de la conjecture de JaegerLinialPayanTarsi, une conjecture de Berger et al, et une autre d'Albouker et al
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Un graphe est un ensemble de noeuds, ensemble de liens reliant des paires de noeuds. Avec la quantité accumulée de données collectées, il existe un intérêt croissant pour la compréhension des structures et du comportement de très grands graphes. Néanmoins, l'augmentation rapide de la taille des grands graphes rend l'étude de tous les graphes de moins en moins efficace. Ainsi, il existe une demande impérieuse pour des méthodes plus efficaces pour étudier de grands graphes sans nécessiter la connaissance de tous les graphes. Une méthode prometteuse pour comprendre le comportement de grands graphes consiste à exploiter des propriétés spécifiques de structures locales, telles que la taille des grappes ou la présence locale d'un motif spécifique, c'estàdire un graphe donné (généralement petit). Un exemple classique de la théorie des graphes (cas avérés de la conjecture d'ErdosHajnal) est que, si un graphe de grande taille ne contient pas de motif spécifique, il doit alors avoir un ensemble de noeuds liés par paires ou non liés, de taille exponentiellement plus grande que prévue. Cette thèse abordera certains aspects de deux questions fondamentales de la théorie des graphes concernant la présence, en abondance ou à peine, d'un motif donné dans un grand graphe :  Le grand graphe peutil être partitionné en copies du motif ?  Le grand graphe contientil une copie du motif ? Nous discuterons de certaines des conjectures les plus connues de la théorie des graphes sur ce sujet: les conjectures de Tutte sur les flots dans les graphes et la conjecture d'ErdosHajnal mentionnée cidessus, et présenterons des preuves pour plusieurs conjectures connexes  y compris la conjecture de BarátThomassen, une conjecture de Haggkvist et Krissell, un cas particulier de la conjecture de JaegerLinialPayanTarsi, une conjecture de Berger et al, et une autre d'Albouker et al
Lattice  Based Cryptography  Security Foundations and Constructions by
Adeline RouxLanglois(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
Latticebased cryptography is a branch of cryptography exploiting the presumed hardness of some wellknown problems on lattices. Its main advantages are its simplicity, efficiency, and apparent security against quantum computers. The principle of the security proofs in latticebased cryptography is to show that attacking a given scheme is at least as hard as solving a particular problem, as the Learning with Errors problem (LWE) or the Small Integer Solution problem (SIS). Then, by showing that those two problems are at least as hard to solve than a hard problem on lattices, presumed polynomial time intractable, we conclude that the constructed scheme is secure.In this thesis, we improve the foundation of the security proofs and build new cryptographic schemes. We study the hardness of the SIS and LWE problems, and of some of their variants on integer rings of cyclotomic fields and on modules on those rings. We show that there is a classical hardness proof for the LWE problem (Regev's prior reduction was quantum), and that the module variants of SIS and LWE are also hard to solve. We also give two new latticebased group signature schemes, with security based on SIS and LWE. One is the first latticebased group signature with logarithmic signature size in the number of users. And the other construction allows another functionality, verifierlocal revocation. Finally, we improve the size of some parameters in the work on cryptographic multilinear maps of Garg, Gentry and Halevi in 2013
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
Latticebased cryptography is a branch of cryptography exploiting the presumed hardness of some wellknown problems on lattices. Its main advantages are its simplicity, efficiency, and apparent security against quantum computers. The principle of the security proofs in latticebased cryptography is to show that attacking a given scheme is at least as hard as solving a particular problem, as the Learning with Errors problem (LWE) or the Small Integer Solution problem (SIS). Then, by showing that those two problems are at least as hard to solve than a hard problem on lattices, presumed polynomial time intractable, we conclude that the constructed scheme is secure.In this thesis, we improve the foundation of the security proofs and build new cryptographic schemes. We study the hardness of the SIS and LWE problems, and of some of their variants on integer rings of cyclotomic fields and on modules on those rings. We show that there is a classical hardness proof for the LWE problem (Regev's prior reduction was quantum), and that the module variants of SIS and LWE are also hard to solve. We also give two new latticebased group signature schemes, with security based on SIS and LWE. One is the first latticebased group signature with logarithmic signature size in the number of users. And the other construction allows another functionality, verifierlocal revocation. Finally, we improve the size of some parameters in the work on cryptographic multilinear maps of Garg, Gentry and Halevi in 2013
Etude structurelle et algorithmique des graphes pouvant être séparés avec des plus courts chemins by
Emilie Diot(
)
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
Les graphes sont des objets couramment utilisés pour modéliser de nombreuses situations réelles comme des réseaux routiers, informatiques ou encore électriques. Ils permettent de résoudre des problèmes sur ces réseaux comme le routage (aller d'un sommet à un autre en suivant les arêtes du graphe) ou encore leur exploration (obtenir une carte du graphe étudié). Les réseaux étudiés, et donc les graphes qui les modélisent, peuvent être grands, c'estàdire avoir un très grand nombre de sommets. Dans ce cas, comme dans le cas de l'étude de grandes données en général, nous pouvons utiliser le paradigme << Diviser pour mieux régner >> pour répondre aux questions posées. En effet, en travaillant sur des petites parties du graphe et en fusionnant les résultats obtenus sur ces petites parties, on peut obtenir le résultat sur le graphe global. Dans ce document, nous présenterons une manière de décomposer les graphes en utilisant des plus courts chemins comme séparateurs. Cette décomposition permet d'obtenir, par exemple, un routage efficace, un étiquetage compacte pour pouvoir estimer les distances entre les sommets d'un graphe ou encore une navigation efficace dans les graphes<< petit monde >>. Cette méthode va nous permettre de définir de nouvelles classes de graphes
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
Les graphes sont des objets couramment utilisés pour modéliser de nombreuses situations réelles comme des réseaux routiers, informatiques ou encore électriques. Ils permettent de résoudre des problèmes sur ces réseaux comme le routage (aller d'un sommet à un autre en suivant les arêtes du graphe) ou encore leur exploration (obtenir une carte du graphe étudié). Les réseaux étudiés, et donc les graphes qui les modélisent, peuvent être grands, c'estàdire avoir un très grand nombre de sommets. Dans ce cas, comme dans le cas de l'étude de grandes données en général, nous pouvons utiliser le paradigme << Diviser pour mieux régner >> pour répondre aux questions posées. En effet, en travaillant sur des petites parties du graphe et en fusionnant les résultats obtenus sur ces petites parties, on peut obtenir le résultat sur le graphe global. Dans ce document, nous présenterons une manière de décomposer les graphes en utilisant des plus courts chemins comme séparateurs. Cette décomposition permet d'obtenir, par exemple, un routage efficace, un étiquetage compacte pour pouvoir estimer les distances entre les sommets d'un graphe ou encore une navigation efficace dans les graphes<< petit monde >>. Cette méthode va nous permettre de définir de nouvelles classes de graphes
Autour du problème du Domino  Structures combinatoires et outils algébriques by
Etienne Moutot(
)
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
Given a finite set of square tiles, the domino problem is the question of whether is it possible ta tile the plane using these tiles.This problem is known to be undecidable in the planar case, and is strongly linked ta the question of the periodicity of the tiling.ln this thesis we look at this problem in two different ways: we look at the particular case of low complexity tilings and we generalize it to more general structures than the plane: groups.A tiling of the plane is sa id of low complexity if there are at most mn rectangles of size m x n appearing in it. Nivat conjectured in 1997 that any such tiling must be periodic, with the consequence that the domino problem would be decidable for low complexity tilings. Using algebraic tools introduced by Kari and Szabados, we prove a generalized version of Nivat's conjecture for a particular class of tilings (a subclass of what is called of algebraic subshifts). We also manage to prove that Nivat's conjecture holds for uniformly recurrent tilings, with the consequence that the domino problem is indeed decidable for lowcomplexity tilings.The domino problem can be formulated in the more general context of Cayley graphs of groups. ln this thesis, we develop new techniques allowing to relate the Cayley graph of some groups with graphs of substitutions on words.A first technique allows us to show that there exists bath strongly periodic and weaklybutnot strongly a periodic tilings of the BaumslagSolitar groups BS(l,n).A second technique is used to show that the domino problem is undecidable for surface groups. Which provides yet another class of groups verifying the conjecture saying that the domino problem of a group is decidable if and only if the group is virtually free
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
Given a finite set of square tiles, the domino problem is the question of whether is it possible ta tile the plane using these tiles.This problem is known to be undecidable in the planar case, and is strongly linked ta the question of the periodicity of the tiling.ln this thesis we look at this problem in two different ways: we look at the particular case of low complexity tilings and we generalize it to more general structures than the plane: groups.A tiling of the plane is sa id of low complexity if there are at most mn rectangles of size m x n appearing in it. Nivat conjectured in 1997 that any such tiling must be periodic, with the consequence that the domino problem would be decidable for low complexity tilings. Using algebraic tools introduced by Kari and Szabados, we prove a generalized version of Nivat's conjecture for a particular class of tilings (a subclass of what is called of algebraic subshifts). We also manage to prove that Nivat's conjecture holds for uniformly recurrent tilings, with the consequence that the domino problem is indeed decidable for lowcomplexity tilings.The domino problem can be formulated in the more general context of Cayley graphs of groups. ln this thesis, we develop new techniques allowing to relate the Cayley graph of some groups with graphs of substitutions on words.A first technique allows us to show that there exists bath strongly periodic and weaklybutnot strongly a periodic tilings of the BaumslagSolitar groups BS(l,n).A second technique is used to show that the domino problem is undecidable for surface groups. Which provides yet another class of groups verifying the conjecture saying that the domino problem of a group is decidable if and only if the group is virtually free
Small degree outbranchings by
Jørgen BangJensen(
Book
)
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
2 editions published in 2001 in English and held by 1 WorldCat member library worldwide
Les piles de sable Kadanoff by
Kévin Perrot(
)
1 edition published in 2013 in French and held by 1 WorldCat member library worldwide
Sandpile models are a subclass of Cellular Automata. Bak et al. introduced them in 1987 for they exemplify the intuitive notion of SelfOrganized Criticality.The Kadanoff sandpile model is a nonlinear discrete dynamical system illustrating the evolution of cubic sand grains from nicely packed columns to nicely packed columns. For a fixed parameter p, a rule is applied until reaching a stable configuration, called a fixed point : if the height difference between two consecutive columns is strictly greater than p, then p grains fall from the left column, one landing on each of the p adjacent columns on the right.From a simple local rule, to describe and understand the macroscopic behavior of sandpiles is very quickly challenging. The difficulty consists in the simultaneous study of continuous and discrete aspects of the system: on a large scale, a sandpile flows like a liquid; but on a small scale, when we want to describe exactly the shape of a fixed point, the effects of the discrete dynamic must be taken into account. If for example we add a single grain on a stabilized sandpile, it triggers an avalanche that roughly changes only the upper layer of the configuration, but which size is hard to predict because it is sensitive to the tiniest change of the configuration.In analogy with an hourglass, we are particularly interested in the sequence of fixed points reached after adding a finite number of grains on one position, with the aim of explaining the emergence of surprisingly regular patterns.After conjecturing the emergence of wave patterns on fixed points, we firstly consider an inductive procedure for computing fixed points. Each step of the induction corresponds to the computation of an avalanche triggered by the addition of a new grain, for which we propose a simple description. This study is carried on with the definition of the trace of avalanches on a column i, which catches in a word among a finite alphabet enough information in order to reconstruct the fixed point on the right of index i. Links between traces on successive columns are then investigated, links allowing to conclude the emergence of regular traces, whose fixed point's reconstruction involves the appearance and maintain of the wave patterns observed. This first approach is conclusive for the smallest conjectured parameter so far, p=2.The study of the general case goes through the design of a new system meddling in different representations of fixed points, which will be analyzed via an association of arguments of linear algebra and combinatorics (respectively corresponding to the continuous and discrete modalities of sandpiles). This result stating the emergence of regularities in a discrete dynamical system put new technics into light, for which the comprehension of a particular point in the proof remains to be increased. This motivates the consideration of a more general frame of work tackling the notion of emergence
1 edition published in 2013 in French and held by 1 WorldCat member library worldwide
Sandpile models are a subclass of Cellular Automata. Bak et al. introduced them in 1987 for they exemplify the intuitive notion of SelfOrganized Criticality.The Kadanoff sandpile model is a nonlinear discrete dynamical system illustrating the evolution of cubic sand grains from nicely packed columns to nicely packed columns. For a fixed parameter p, a rule is applied until reaching a stable configuration, called a fixed point : if the height difference between two consecutive columns is strictly greater than p, then p grains fall from the left column, one landing on each of the p adjacent columns on the right.From a simple local rule, to describe and understand the macroscopic behavior of sandpiles is very quickly challenging. The difficulty consists in the simultaneous study of continuous and discrete aspects of the system: on a large scale, a sandpile flows like a liquid; but on a small scale, when we want to describe exactly the shape of a fixed point, the effects of the discrete dynamic must be taken into account. If for example we add a single grain on a stabilized sandpile, it triggers an avalanche that roughly changes only the upper layer of the configuration, but which size is hard to predict because it is sensitive to the tiniest change of the configuration.In analogy with an hourglass, we are particularly interested in the sequence of fixed points reached after adding a finite number of grains on one position, with the aim of explaining the emergence of surprisingly regular patterns.After conjecturing the emergence of wave patterns on fixed points, we firstly consider an inductive procedure for computing fixed points. Each step of the induction corresponds to the computation of an avalanche triggered by the addition of a new grain, for which we propose a simple description. This study is carried on with the definition of the trace of avalanches on a column i, which catches in a word among a finite alphabet enough information in order to reconstruct the fixed point on the right of index i. Links between traces on successive columns are then investigated, links allowing to conclude the emergence of regular traces, whose fixed point's reconstruction involves the appearance and maintain of the wave patterns observed. This first approach is conclusive for the smallest conjectured parameter so far, p=2.The study of the general case goes through the design of a new system meddling in different representations of fixed points, which will be analyzed via an association of arguments of linear algebra and combinatorics (respectively corresponding to the continuous and discrete modalities of sandpiles). This result stating the emergence of regularities in a discrete dynamical system put new technics into light, for which the comprehension of a particular point in the proof remains to be increased. This motivates the consideration of a more general frame of work tackling the notion of emergence
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Related Identities
 Deuber, Walter A. Author
 SpringerLink (Online service) Other
 École normale supérieure de Lyon Other Degree grantor
 École doctorale en Informatique et Mathématiques de Lyon Other
 Laboratoire de l'informatique du parallélisme (Lyon) Other
 Le, TienNam Other Author
 BangJensen, Jørgen Author
 Université Claude Bernard (Lyon) Degree grantor
 Harutyunyan, Ararat Other Author
 Trotignon, Nicolas Other Opponent Thesis advisor