Contraintes De Partitionnement De Graphe

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Contraintes De Partitionnement De Graphe

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Author : Xavier Lorca
language : fr
Publisher:
Release Date : 2007

Contraintes De Partitionnement De Graphe written by Xavier Lorca and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.

Les problèmes combinatoires basés sur le partitionnement de graphe permettent de modéliser un grand nombre d'applications pratiques. On retiendra des exemples aussi variés que la reconstruction de " super-arbres " en phylogénie, la planification de missions, ou la construction de tournées de véhicules en logistique. Ces applications, bien que provenant de domaines différents, peuvent toutes se voir comme un problème de partitionnement de graphe par des patrons tels que des cycles, des chemins, ou des arbres. Cependant, les problèmes pratiques se résument rarement à des problèmes " pur " comme peuvent l'être le problème de chemin Hamiltonien ou le problème des K-chemins disjoints. En effet, ils combinent bien souvent le problème de partitionnement avec un ensemble de restrictions sur la topologie des sommets et des arcs. La diversité des contraintes opérationnelles misent en jeu constitue souvent une limite à leur résolution par des approches considérant de manière séparée le problème de partitionnement et les restrictions supplémentaires imposées. Cette thèse se concentre sur les problèmes de satisfaction de contraintes liés au partitionnement de graphe par des arbres mettant en jeu un certain nombre de restrictions sur la topologie des partitions autorisées. Notre travail se focalise en particulier sur l'étude des interactions existantes entre le problème de partitionnement et les restrictions classiques (telles que les relations de précédences ou d'incomparabilités entre les sommets du graphe à partitionner). Nous nous attachons plus particulièrement à montrer comment prendre en compte de manière globale un certain nombre de ces restrictions au sein d'une contrainte de partitionnement de graphes par des arbres. Un autre aspect essentiel porte sur la mise en \oe uvre d'une telle contrainte~: nous montrons en quoi une gestion dynamique des structures de données permet de s'abstraire significativement d'un problème récurrent à la plupart des contraintes globales liées aux graphes : la sensibilité des algorithmes de graphes à la densité des graphes pris en paramètre par la contrainte.

Contraintes Globales De Partitionnement De Graphe Par Des Arbres

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Author : Xavier Lorca
language : fr
Publisher: Lavoisier
Release Date : 2011

Contraintes Globales De Partitionnement De Graphe Par Des Arbres written by Xavier Lorca and has been published by Lavoisier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Bond graphs categories.

La 4ème de couverture indique : Les problèmes combinatoires basés sur le partitionnement de graphe permettent de modéliser un grand nombre d'applications pratiques dans des domaines aussi variés que la planification de missions ou la construction de tournées de véhicules en logistique. Ces applications peuvent toutes être considérées comme un problème de partitionnement de graphe par des patrons tels que des cycles, des chemins ou des arbres.

Contributions Des Probl Mes De Partitionnement De Graphe Sous Contraintes De Ressources

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Author : Dang Phuong Nguyen
language : en
Publisher:
Release Date : 2016

Contributions Des Probl Mes De Partitionnement De Graphe Sous Contraintes De Ressources written by Dang Phuong Nguyen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.

The graph partitioning problem is a fundamental problem in combinatorial optimization. The problem refers to partitioning the set of nodes of an edge weighted graph in several disjoint node subsets (or clusters), so that the sum of the weights of the edges whose end-nodes are in different clusters is minimized. In this thesis, we study the graph partitioning problem on graph with (non negative) node weights with additional set constraints on the clusters (GPP-SC) specifying that the total capacity (e.g. the total node weight, the total capacity over the edges having at least one end-node in the cluster) of each cluster should not exceed a specified limit (called capacity limit). This differs from the variants of graph partitioning problem most commonly addressed in the literature in that:-The number of clusters is not imposed (and is part of the solution),-The weights of the nodes are not homogeneous.The subject of the present work is motivated by the task allocation problem in multicore structures. The goal is to find a feasible placement of all tasks to processors while respecting their computing capacity and minimizing the total volume of interprocessor communication. This problem can be formulated as a graph partitioning problem under knapsack constraints (GPKC) on sparse graphs, a special case of GPP-SC. Moreover, in such applications, the case of uncertain node weights (weights correspond for example to task durations) has to be taken into account.The first contribution of the present work is to take into account the sparsity character of the graph G = (V,E). Most existing mathematical programming models for the graph partitioning problem use O(|V|^3) metric constraints to model the partition of nodes and thus implicitly assume that G is a complete graph. Using these metric constraints in the case where G is not complete requires adding edges and constraints which may greatly increase the size of the program. Our result shows that for the case where G is a sparse graph, we can reduce the number of metric constraints to O(|V||E|).The second contribution of present work is to compute lower bounds for large size graphs. We propose a new programming model for the graph partitioning problem that make use of only O(m) variables. The model contains cycle inequalities and all inequalities related to the paths in the graph to formulate the feasible partitions. Since there are an exponential number of constraints, solving the model needs a separation method to speed up the computation times. We propose such a separation method that use an all pair shortest path algorithm thus is polynomial time. Computational results show that our new model and method can give tight lower bounds for large size graphs of thousands of nodes.....

Contraintes Globales De Partitionnement De Graphe Par Des Arbres

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Author : Lorca
language : fr
Publisher: Lavoisier
Release Date : 2011

Contraintes Globales De Partitionnement De Graphe Par Des Arbres written by Lorca and has been published by Lavoisier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

Traitement De Contraintes Sur Les Graphes En Programmation Par Contraintes

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Author : Eric Bourreau
language : fr
Publisher:
Release Date : 1999

Traitement De Contraintes Sur Les Graphes En Programmation Par Contraintes written by Eric Bourreau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

L'OBJET DE CETTE THESE EST LE TRAITEMENT DE CONTRAINTES SUR LES GRAPHES DANS LE CADRE DE LA PROGRAMMATION PAR CONTRAINTES (PPC). L'IMPORTANCE DE LA PROBLEMATIQUE DE RECOUVREMENT D'UN GRAPHE PAR DES CIRCUITS EST ISOLEE AFIN DE POUVOIR SATISFAIRE DE NOMBREUSES DEMANDES INDUSTRIELLES MODELISEES EN PPC, NOTAMMENT POUR LES TOURNEES. NOUS PRESENTONS LA CONTRAINTE DITE CYCLE QUI CONSTITUE UNE REPONSE A CES BESOINS. LA PREMIERE VARIANTE CYCLE (N, G, W, MIN, MAX) ETABLIE QUE LA CONTRAINTE DOIT SATISFAIRE LE PARTITIONNEMENT DES NUDS D'UN GRAPHE ORIENTE G PAR N CIRCUITS DISJOINTS DONT LA SOMME DES POIDS W DES NUDS VARIE ENTRE MIN ET MAX. CEPENDANT, POUR REPONDRE AUX PARTICULARITES INDUSTRIELLES, UNE SERIE DE CONCEPTS A ETE INTRODUITS SOUS FORME DE PARAMETRES ADDITIONNELS ; DES PRECEDENCES INDIRECTES RAISONNENT SUR UNE VISION TEMPORELLE, UNE MATRICE DE DISTANCES APPORTE UNE VISION GEOGRAPHIQUE ; DES CAPACITES, POSITIVES OU NEGATIVES, APPLIQUEES AUX NUDS DU GRAPHE ETENDENT UNE VISION CUMULATIVE. LA PRISE EN COMPTE DES CONTRAINTES REGLEMENTAIRES CONDUIT A LA DEFINITION DES CONCEPTS DE MOTIFS ET DE SHIFT. L'APPARITION DE CERTAINS MOTIFS SUR LES CHEMINEMENTS EST INTERDITE PAR LE PARAMETRE SEQUENCE ; QUANT AU PARAMETRE SHIFT, IL PERMET LA GESTION D'INSERTION DE REPOS OBLIGATOIRES ENTRE DES PERIODES DE TRAVAIL. D'UN POINT DE VUE ACADEMIQUE, LA CONTRAINTE CYCLE PERMET DE RESOUDRE DES PROBLEMES REPUTES DIFFICILES. DE PLUS, DES RESULTATS INTERESSANTS ONT ETE MIS A JOUR SUR LE CAVALIER D'EULER GENERALISE. D'UN POINT DE VUE PRATIQUE, LA CONTRAINTE CYCLE A SERVIT POUR LA REALISATION D'APPLICATIONS INDUSTRIELLES DANS LE DOMAINE DES PROBLEMES DE TOURNEES DE VEHICULES, DE CHARGEMENT/DECHARGEMENT, DE SEQUENCEMENT DE PRODUCTION ET DES ROTATIONS D'EQUIPAGE. CES TRAVAUX DE THESE REALISES DANS LE CADRE DE LA PROGRAMMATION PAR CONTRAINTES, MOTIVES PAR DES BESOINS INDUSTRIELS ONT PERMIS A LA FOIS DE REVISITER CERTAINS ALGORITHMES DE GRAPHES TOUT EN CHERCHANT UN EQUILIBRE ENTRE EXPRESSIVITE ET PERFORMANCE.

Graph Partitioning

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Author : Charles-Edmond Bichot
language : en
Publisher: John Wiley & Sons
Release Date : 2013-01-24

Graph Partitioning written by Charles-Edmond Bichot and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-24 with Computers categories.

Graph partitioning is a theoretical subject with applications in many areas, principally: numerical analysis, programs mapping onto parallel architectures, image segmentation, VLSI design. During the last 40 years, the literature has strongly increased and big improvements have been made. This book brings together the knowledge accumulated during many years to extract both theoretical foundations of graph partitioning and its main applications.

Approximation De Probl Mes De Couverture Et De Partitionnement De Graphes

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Author : Laurent Alfandari
language : fr
Publisher:
Release Date : 1999

Approximation De Probl Mes De Couverture Et De Partitionnement De Graphes written by Laurent Alfandari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

PARMI LES PROBLEMES D'OPTIMISATION, LES PROBLEMES NP-DIFFICILES SONT TELS QUE LES SEULES METHODES CONNUES DE RESOLUTION EXACTE SONT DES ALGORITHMES DE COMPLEXITE EXPONENTIELLE, INDUISANT DES TEMPS DE CALCUL SOUVENT PROHIBITIFS POUR DES PROBLEMES DE TRES GRANDE TAILLE. LA THEORIE DE L'APPROXIMATION POLYNOMIALE, QUI EST LE CADRE D'ETUDE DE CETTE THESE, CHERCHE A CONCEVOIR POUR CES PROBLEMES DES ALGORITHMES APPROCHES, DE COMPLEXITE POLYNOMIALE, AVEC GARANTIE DE PERFORMANCE, I.E. FOURNISSANT UNE SOLUTION NON TOUJOURS OPTIMALE MAIS DONT ON SOUHAITE POUVOIR BORNER A PRIORI LA VALEUR RELATIVEMENT A L'OPTIMUM. NOUS TRAITONS PARTICULIEREMENT DES PROBLEMES D'OPTIMISATION COMBINATOIRE DANS DES GRAPHES, CONSISTANT A COUVRIR OU PARTITIONNER LES SOMMETS OU LES ARETES D'UN GRAPHE PAR DES SOUS-GRAPHES. NOUS DEFINISSONS AINSI LA CLASSE MST DES PROBLEMES MAITRE-ESCLAVE APPROXIMABLES, DONT NOUS MONTRONS QU'ILS SE REDUISENT AU PROBLEME CLASSIQUE DE SET COVERING PAR UNE NOUVELLE FORME DE REDUCTION PRESERVANT L'APPROXIMATION APPELEE PSEUDO-REDUCTION. NOUS EN DEDUISONS L'INCLUSION DE LA CLASSE MST DANS LA CLASSE APX LOGN DES PROBLEMES APPROXIMABLES A RAPPORT LOGARITHMIQUE. NOUS ETENDONS L'UTILISATION DE CETTE APPROCHE ET DE NOTRE PSEUDO-REDUCTION A L'APPROXIMATION DE PROBLEMES DE PACKING DE GRAPHES. NOUS MONTRONS QUE L'APPROCHE MAITRE-ESCLAVE S'APPLIQUE A DE NOMBREUX PROBLEMES D'OPTIMISATION, TELS QUE LE PROBLEME DE LA FORET RECOUVRANTE MINIMUM DE DIAMETRE BORNE, UN PROBLEME DE COUVERTURE DES ARETES PAR DES ARBRES, CERTAINES RESTRICTIONS DU PROBLEME DE CONSTRUCTION DE ROTATIONS, AINSI QUE LE PROBLEME DE L'ARBRE RECOUVRANT DE POIDS MINIMUM DE PROFONDEUR 2, POUR LEQUEL NOUS FOURNISSONS DIVERS RESULTATS D'APPROXIMATION DEPASSANT LE CADRE DE LA CLASSE MST. FINALEMENT, NOUS NOUS INTERESSONS A LA FORMULATION LOGIQUE DES PROBLEMES DE COUVERTURE ET DE PARTITIONNEMENT DANS LE CADRE DE L'APPROXIMATION POLYNOMIALE, ET CONCLUONS SUR UNE NOUVELLE HIERARCHIE DE CLASSES A L'INTERIEUR DE LA CLASSE APX LOGN.

Tree Based Graph Partitioning Constraint

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Author : Xavier Lorca
language : en
Publisher: John Wiley & Sons
Release Date : 2013-01-24

Tree Based Graph Partitioning Constraint written by Xavier Lorca and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-24 with Mathematics categories.

Combinatorial problems based on graph partitioning enable us to mathematically represent and model many practical applications. Mission planning and the routing problems occurring in logistics perfectly illustrate two such examples. Nevertheless, these problems are not based on the same partitioning pattern: generally, patterns like cycles, paths, or trees are distinguished. Moreover, the practical applications are often not limited to theoretical problems like the Hamiltonian path problem, or K-node disjoint path problems. Indeed, they usually combine the graph partitioning problem with several restrictions related to the topology of nodes and arcs. The diversity of implied constraints in real-life applications is a practical limit to the resolution of such problems by approaches considering the partitioning problem independently from each additional restriction. This book focuses on constraint satisfaction problems related to tree partitioning problems enriched by several additional constraints that restrict the possible partitions topology. On the one hand, this title focuses on the structural properties of tree partitioning constraints. On the other hand, it is dedicated to the interactions between the tree partitioning problem and classical restrictions (such as precedence relations or incomparability relations between nodes) involved in practical applications. Precisely, Tree-based Graph Partitioning Constraint shows how to globally take into account several restrictions within one single tree partitioning constraint. Another interesting aspect of this book is related to the implementation of such a constraint. In the context of graph-based global constraints, the book illustrates how a fully dynamic management of data structures makes the runtime of filtering algorithms independent of the graph density.

Restriction Of Graph Partition Problems

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Author : Hans L. Bodlaender
language : en
Publisher:
Release Date : 1991

Restriction Of Graph Partition Problems written by Hans L. Bodlaender and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.

Integration Of Ai And Or Techniques In Constraint Programming

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Author : Domenico Salvagnin
language : en
Publisher: Springer
Release Date : 2017-05-30

Integration Of Ai And Or Techniques In Constraint Programming written by Domenico Salvagnin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-30 with Computers categories.

This book constitutes the proceedings of the 14th International Conference on Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2017, held in Padua, Italy, in June 2017. The 32 full papers presented together with 6 abstracts were carefully reviewed and selected from numerous submissions. The conference brings together interested researchers from constraint programming, artificial intelligence, and operations research to present new techniques or applications in the intersection of these fields and provides an opportunity for researchers in one area to learn about techniques in the others, and to show how the integration of techniques from different fields can lead to interesting results on large and complex problems.