大型災害頻傳傷亡慘重，若能把握於救災黃金72小時內救出受困民眾，則可望挽回更多寶貴的生命，但災區通訊網路基礎設施常因災害而遭受嚴重損毀，無法正常運作。救災工作在缺乏通訊系統的支援下，因溝通協調的困難而紊亂無章、效率低落。 本研究提出一個可快速恢復特定區域通訊服務的網路，並為其設計通訊的拓撲結構。我們稱該網路為應急蜂巢式行動通訊網路(Contingency Cellular Network)，簡稱CCN網路。CCN網路利用無線電連接災區行動電話網路中斷訊但結構未損的基地台建構而成，具有建置速度快、使用門檻低等多項特點，可支援災區救援的緊急通訊。 本研究中，我們以各毀損基地台通訊範圍內的通訊需求人數與災區毀損程度，作為效益參數，嘗詴在蜂巢式網路的格網架構以及數量有限的緊急通訊設備下，選擇效益較高的位置點配置緊急通訊設備，建立應急蜂巢式行動網路的網路拓撲，此拓撲除追求最大救災效益外，並顧及通訊品質，避免建立負載失衡的連線。我們將問題塑模為一類似圖論中的K-Minimum Cost Spanning Tree (K-Cardinality Tree or KCT)問題，稱為Depth Bounded K-Maximum Profit Spanning Tree問題，並提供數個快速的啟發式演算法，可在緊急時快速地建立應急蜂巢式行動網路拓撲。 / When a catastrophic natural disaster occurs, the efficiency of disaster response operation is critical to life saving. However, communication systems, such as cellular networks, usually crashed due to various causes that make coordination difficult for many disorganized disaster response workers extremely. Unfortunately, rapid deployment of many existing emergency communication systems relies on a good transportation system, which is usually not available in a catastrophic natural disaster. We propose a Contingency Cellular Network (CCN) by connecting disconnected base stations together with wireless links and portable power generators. CCN can support existing mobile phone users with limited capability. Such a system can support a large number of voluntary workers in the early hours of a catastrophic natural disaster, thus saving many lives. Communication traffics, either voice or data, are forwarded hop-by-hop to the external network that remains operational. The efficiency and effeteness of CCN is obviously depends on the topology of such a forwarding network. This thesis addresses the design of forwarding topology aiming to maximize its efficiency. We take the degree of emergency degree of the damage, population of each stricken as the priority measure as well as the amount of emergency recovery resources as the constraint to determine the topology. We model the CCN topology design problem into a Depth Bounded K-Maximum Spanning Tree Problem. The problem is proven NP-hard and we designed an efficient heuristic algorithm (DBTB) to solve it. We also model CCN topology design problem into a Hop Concerned K-Maximum Spanning iii Tree Program and designed a HCTB algorithm to solve it. The simulation results show that DBTB algorithm can control tree depth effectively but HCTB can gain more profit.

Submitted by Felipe Rodrigues de Menezes Tomaz (felipetomaz@gmail.com) on 2017-03-08T18:07:35Z No. of bitstreams: 1 Dissertação - Final.pdf: 1323190 bytes, checksum: c28bd29047e066ff34bb9203c46e9fec (MD5) / Rejected by Renata de Souza Nascimento (renata.souza@fgv.br), reason: Felipe, boa noite Por gentileza, realizar as seguintes alterações para que possamos aceitar seu trabalho: Retirar a acentuação do nome Getúlio Centralizar os títulos: Dedicatória, Resumo e Abstract. O título está diferente com o que consta em Ata e nenhuma solicitação do orientador. Neste caso, iremos entrar em contato para que o mesmo confirme a alteração. Em seguida, deverá submeter o arquivo novamente. Att on 2017-03-08T23:14:39Z (GMT) / Submitted by Felipe Rodrigues de Menezes Tomaz (felipetomaz@gmail.com) on 2017-03-09T12:57:43Z No. of bitstreams: 1 Dissertação - Final.pdf: 1323164 bytes, checksum: 26add34e2f577cfcec02f52da04b7845 (MD5) / Rejected by Renata de Souza Nascimento (renata.souza@fgv.br), reason: Felipe, boa tarde Em contato com o prof. Ricardo Rochman, o mesmo confirma que não solicitou e não autoriza a mudança no título do trabalho. Deverá retornar ao título que consta em Ata e protocolo inicial: ESTUDO DE UTILIZAÇÃO DE UMA MINIMUM SPANNING TREE DE CORRELAÇÕES COMO SELETORA DE AÇÕES EM UMA ESTRATÉGIA DE COINTEGRAÇÃO NO MERCADO DE BRASILEIRO Att. on 2017-03-09T16:15:49Z (GMT) / Submitted by Felipe Rodrigues de Menezes Tomaz (felipetomaz@gmail.com) on 2017-03-09T19:35:28Z No. of bitstreams: 1 Dissertação - Final.pdf: 1322284 bytes, checksum: 9ec2cbcae5a0293ac6a12c5a9ae85ebf (MD5) / Approved for entry into archive by Renata de Souza Nascimento (renata.souza@fgv.br) on 2017-03-09T19:40:49Z (GMT) No. of bitstreams: 1 Dissertação - Final.pdf: 1322284 bytes, checksum: 9ec2cbcae5a0293ac6a12c5a9ae85ebf (MD5) / Made available in DSpace on 2017-03-10T13:02:47Z (GMT). No. of bitstreams: 1 Dissertação - Final.pdf: 1322284 bytes, checksum: 9ec2cbcae5a0293ac6a12c5a9ae85ebf (MD5) Previous issue date: 2017-02-10 / This work aimed to evaluate the possibility of using a miminum spanning tree (MST) of correlation between assets as a selection tool in a pairs trading strategy based on cointegration. From a selection of Bovespa exchange index assets, cointegration tests were performed between pairs of assets and, subsequently, starting from positive results, backtestings were executed. After that, the backtestings were filtered by information included in an MST. For a given period, when a cointegration was found between a pair of assets, a MST was developed and it was analyzed if there was a direct link between those assets in the MST’s structure. Otherwise, the backtesting result from the cointegration would be disregarded. By comparing the total set of results with the subset of results that took into account the MST constraint, it was evaluated the impact of the use of the MST, as an asset selector, on the result of the pairs trading strategy. / Essa dissertação teve como objetivo avaliar a possibilidade de utilização de uma miminum spanning tree (MST) de correlação entre ativos como instrumento de seleção em uma estratégia de pairs trading que teve como base a cointegração. A partir de uma seleção de ativos do índice Bovespa, foram feitos testes de cointegração entre pares de ativos e, posteriormente, partindo de resultados positivos, foram executados backtestings que foram filtrados por informações provenientes de uma MST. Para determinado período, ao se encontrar uma cointegração entre um par dos ativos considerados, uma MST foi desenvolvida e analisou-se a existência de um link direto entre o par de ativos na estrutura da MST. Caso contrário, o resultado do backtesting proveniente desta cointegração foi desconsiderado. Fazendo-se a comparação do conjunto total de resultados com o subconjunto de resultados que levam em consideração a restrição da MST, avaliou-se o impacto da utilização da MST, como seletora de ativos, no resultado da estratégia de pairs trading.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The generalized minimum spanning tree problem is present in several situations of the real world, such as in the context of the telecommunications, transports and grouping of data, where a net of necessary clusters to be connected using a node of each cluster. In that work it is presented the project and the implementation of an algorithm of tabu search with path relinking and iterated local search for the generalized minimum spanning tree problem and your variant with at least one vertex by group. In the computational tests 271 instances of TSPLIB were used generated through the grouping methods Center Clustering and Grid Clustering, and more 20 instances for the extension of the problem with at least one vertex by group. The results demonstrate the efficiency of the algorithm proposed in the obtaining of satisfactory solutions for the two problems. / O problema da árvore geradora mínima generalizado está presente em várias situações do mundo real, tais como no contexto das telecomunicações, transportes e agrupamento de dados, nas quais uma rede de grupos precisa ser conectada utilizando um nodo de cada grupo. Nesse trabalho é apresentado o projeto e a implementação de um algoritmo de busca tabu com reconexão de caminhos e busca local iterativa para o problema da árvore geradora mínima generalizado e sua variante com pelo menos um vértice por grupo. Nos testes computacionais foram utilizadas 271 instâncias da TSPLIB geradas através dos métodos de agrupamento Center Clustering e Grid Clustering, e mais 20 instâncias para a extensão do problema com pelo menos um vértice por grupo. Os resultados demonstram a eficiência do algoritmo proposto na obtenção de soluções satisfatórias para os dois problemas.

Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-09-21T13:50:00Z No. of bitstreams: 1 TeseCCMT.pdf: 3540141 bytes, checksum: e392913d01ce26b3d8bd932aa7e84611 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2016-09-27T19:31:27Z (GMT) No. of bitstreams: 1 TeseCCMT.pdf: 3540141 bytes, checksum: e392913d01ce26b3d8bd932aa7e84611 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2016-09-27T19:31:38Z (GMT) No. of bitstreams: 1 TeseCCMT.pdf: 3540141 bytes, checksum: e392913d01ce26b3d8bd932aa7e84611 (MD5) / Made available in DSpace on 2016-09-27T19:42:35Z (GMT). No. of bitstreams: 1 TeseCCMT.pdf: 3540141 bytes, checksum: e392913d01ce26b3d8bd932aa7e84611 (MD5) Previous issue date: 2015-03-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The generation of Reactive Production Scheduling (PRP) in order to minimize the makespan is an important activity in the manufacturing industry, in view of the numerous articles reflecting this search today. Among these studies highlight the global search use in hybridization or collaboration with local search, especially of Genetic Algorithm (GA) with Variable Neighborhood Search (VNS). But see that the neighborhood structures used are not related to the goal of makespan minimization or when they are, are difficult to obtain. In order to cover this topic, this thesis proposes the hypothesis that a strongly correlated neighborhood structure with objective of makespan minimization in PRP problems, based on spanning tree, and applied on a collaboration among a genetic algorithm with VNS, perform better or equal to those obtained by other studies using other neighborhood structures or without the use of local search. The purpose was to construct a collaboration of GA and VNS using a neighborhood structure based on the mapping of the solution in the spanning tree associated with the problem, in the local search time, and operating with the insert, swap and 2-opt operators. The planning of experiments for validation contemplated since the implementation and comparison of four variants of reactive production scheduling in three job shop scenarios of different sizes. Each pair of comparisons had its calculated sample size and has been tested with the appropriate hypothesis test. The four variants were compared: Genetic Algorithm only and three collaborations of GA with VNS using the neighborhood structure proposal and two other neighborhood structures (Critical Path and Natural Representation) found in the literature review. The scenarios came from Taillard base. The tests corroborate the hypothesis, with 95% confidence, compared to other works and the main contribution of this thesis is to create an efficient method for minimizing makespan in PRP. / A geração de Programação Reativa da Produção (PRP), com o objetivo de minimizar o makespan, é uma atividade importante na indústria manufatureira, tendo em vista os numerosos artigos que abordam esta pesquisa na atualidade. Dentre estas pesquisas, destaca-se o uso de hibridização ou colaboração de busca global com busca local, notadamente de Algoritmo Genético (AG) com Variable Neighborhood Search (VNS). Porém, nota-se que as estruturas de vizinhança utilizadas não são correlatas à função de minimização de makespan ou, quando o são, são de difícil obtenção. Com o intuito de cobrir tal tópico, esta tese propõe a hipótese de que uma estrutura de vizinhança fortemente correlata ao objetivo de minimização de makespan em problemas de PRP, baseando-se em árvore de cobertura e aplicada em uma colaboração de algoritmo genético e VNS, obtém resultados melhores aos obtidos por outros trabalhos, que fazem uso de outras estruturas de vizinhança ou que não utilizam a busca local. A proposta é a construção de um método de colaboração entre AG e VNS usando uma estrutura de vizinhança baseada no mapeamento da solução, em tempo de busca local, na árvore de cobertura associada ao problema, atuando com os operadores insert, swap e 2-opt. O planejamento dos experimentos para validação contempla a execução e comparação de quatro variantes de solução de problemas de Programação Reativa da Produção em três cenários de job shop de diversas dimensões. Cada par de comparações tem seu tamanho amostral calculado e é examinado com o teste de hipótese adequado. As quatro variantes comparadas são: Algoritmo Genético e três colaborações entre Algoritmo Genético e Variable Neighborhood Search (VNS) usando a estrutura de vizinhança proposta e outras duas estruturas de vizinhança (Caminho Crítico e Representação Natural) encontradas na revisão da literatura. Os cenários vem da base Taillard. Os testes corroboram a hipótese com 95% de confiança na comparação com outros trabalhos e a principal contribuição desta tese é a criação de um método eficiente para minimização de makespan em PRP.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / Introduzimos o problema de Ãrvore Geradora com DependÃncias MÃnima, AGDM(G,D,w), definido sobre um grafo G(V,E) e um digrafo D(E,A), cujos vÃrtices sÃo as arestas de G e cujos arcos definem dependÃncias entre tais arestas. O problema consiste em encontrar, dentre as Ãrvores geradoras do grafo G(V,E) que satisfaÃam as restriÃÃes de dependÃncia impostas pelo digrafo de entrada D(E,A), uma que tenha custo mÃnimo, segundo a ponderaÃÃo w das arestas de G. As restriÃÃes de dependÃncia exigem que uma aresta e de G sà pode fazer parte de uma soluÃÃo se for uma fonte em D ou se fizer parte da soluÃÃo alguma outra aresta à tal que o arco (e′, e) esteja em D. Provamos que decidir se hà soluÃÃo viÃvel para AGDM(G,D,w) à um problema NP-completo, mesmo quando G à um cacto cordal e D à a uniÃo de arborescÃncias de altura no mÃximo 2. Sua NP-completude tambÃm à mostrada ainda que G seja bipartido, as restriÃÃes de dependÃncia ocorram apenas entre arestas adjacentes de G e formem arborescÃncias de altura no mÃximo 2. Resultados idÃnticos sÃo obtidos para as variantes do problema onde, nas restriÃÃes de dependÃncia, substitui-se o requisito âalgumaâ por âexatamente umaâ ou âtodaâ. Para resolver o problema, apresentamos algumas formulaÃÃes de programaÃÃo inteira e desigualdades vÃlidas. Propomos uma estratÃgia para reduzir a dimensÃo do problema, excluindo arestas de G com base na estrutura de D. Avaliamos os modelos e algoritmos propostos usando instÃncias geradas aleatoriamente. Resultados computacionais sÃo reportados. / We introduce the Dependency Constrained Minimum Spanning Tree Problem, DCMST(G,D,w), defined over a graph G(V,E) and a digraph D(E,A), whose vertices are the edges of G and whose arcs describe dependency relations between these edges. Such problem consists of finding, among the spanning trees of G(V,E) satisfying the dependency constraints imposed by D(E,A), that one whose cost is minimum, according to a edgeweight function w. The dependency constraints impose that an edge e of G can be part of a solution either if it is a source in D or if some other edge e′, such that the arc (e′, e) is in D, is part of it as well. We prove that deciding whether there is a feasible solution to DCMST(G,D,w) is an NP-complete problem, even if G is a chordal cactus and D is a union of arborescences of height at most 2. NP-completeness also applies if G is bipartite, the dependency constraints occur only between adjacent edges of G and their related arcs describe arborescences whose height is at most 2. The same results are obtained for the problem variants which demand that, instead of âsomeâ, âexactly oneâor âallâdependencies be part of a solution. To solve the problem, we introduce some integer programming formulations and some valid inequalities. We propose a strategy to reduce the problem dimension by excluding some edges of G according to the structure of D. We evaluate the introduced models and algorithms using randomly generated instances. Computational results are reported.

This thesis focuses on redundancy in data networks and on technologies which are used to achieve high availability in network infrastructure. This thesis is based on industry standards published by well-known standardization authorities. One proprietary technology which can effectively replace these standards and simplify the whole network is also presented in more detail. The theoretical part individually describes all such technologies and standards. The practical part deals with an appropriate combination of these technologies and their application in a specific product environment. This work is meant to describe the whole concept of high availability in network infrastructure and should be instrumental in understanding how these technologies are deployed in practice.

Neste trabalho foi analisada a influência de um evento sobre o mercado de ações brasileiro a partir das redes, e suas árvores geradoras mínimas, obtidas de medidas de dependência baseadas nas correlações de Pearson, de Spearman e de Kendall. O evento considerado foi a notícia da noite de 17 de maio de 2017 em que o dono da empresa brasileira JBS, Joesley Batista, gravou o então Presidente da República Michel Temer autorizando a compra do silêncio de um Deputado Federal. O dia seguinte a notícia, 18 de maio de 2017, foi definido como o dia do evento. Foram coletados dados de alta frequência de 58 ações do Ibovespa no período de 11 a 25 de maio de 2017. As alterações nas redes das ações do mercado foram analisadas comparando-se o período anterior e posterior ao evento em duas escalas de tempo: (1) Redes diárias: cinco pregões antes do evento, o dia do evento e, cinco pregões depois do evento, com cotações a cada 15 minutos; (2) Agrupadas em antes e depois: agrupando os dados dos 5 dias antes e dos 5 dias depois do evento. O estudo das redes diárias indicou mudança de tendência nas suas propriedades no decorrer do período que contém o evento, com cotações a cada 15 minutos. Isto sugeriu que análise do efeito médio contido nos dados agrupados antes de depois do evento poderiam tornar mais evidente as mudanças na estrutura de rede das ações. As redes antes e depois do evento apresentaram mudanças significativas nas suas métricas que ficaram mais evidenciadas nas árvores geradoras mínimas. As redes geradas pelas correlações de Kendall e Spearman apresentaram um número maior de agrupamentos antes e depois do evento e, após o evento, as árvores geradoras mínimas apresentaram uma redução do número de agrupamentos de ações para todos os tipos de correlação. As distribuições de grau ponderado após o evento indicam uma probabilidade maior de vértices com graus distante da média. As métricas das árvores geradoras mínimas por correlação de Spearman sofreram a maior variação, seguidas pelas de Kendall e Pearson, e também, indicaram que as redes após o evento ficaram mais robustas, ou seja, mais rígidas. A maior robustez das redes após o evento indica maior conectividade do mercado, tornando-o, como um todo, mais suscetível ao impacto de novos acontecimentos. / In this work the influence of an event on the Brazilian stock market was analyzed from networks and its minimum spanning trees obtained from measures of dependence based on the Pearson, Spearman, and Kendall\'s correlations. The event considered was the news in the evening of May 17, 2017 in which the owner of the Brazilian company JBS, Joesley Batista, recorded the Brazilian President Michel Temer authorizing the purchase of the silence of a congress member. The day just after the news, May 18, 2017, was defined as the event day. High-frequency data from 58 Ibovespa shares were collected from 11 to 25 May 2017. Changes in the stocks networks were analyzed comparing the period before and after the event in two time scales: (1) Daily networks: five trade sections before the event, the day of the event and, five trade sections after the event, with price every 15 minutes; (2) Grouped before and after do evento: grouping data from 5 days before and 5 days after event. The study of the daily networks indicated a change of trend in their properties during the period that contains the event, with quotations every 15 minutes. The study of daily networks indicated a change of trend in their properties during the period containing the event. This suggested that analysis of the mean effect of grouped data before and after the event could highlight the changes in the network structure. The networks before and after the event showed significant changes in their metrics, which became more evident from the minimum spanning trees. After the event, the minimum spanning trees for grouped data got a smaller number of clusters in the networks for all kind of correlations. The networks generated by Kendall and Spearman correlations presented a larger number of clusters before and after the event. The weighted degree distributions after the event suggest a power law decay tail for all the correlations considered and indicates a higher probability of vertices with weighted degrees far away from the mean weighted degree. The minimum spanning tree metrics generated by Spearman correlation suffered the greatest variation, followed by those of Kendall and Pearson; and their values indicates that after the event the networks became more robust, that is, more rigid. The increase in the networks robustness after the event indicates a higher market connectivity, making it as a whole, more susceptible to the impact of new events.

Cette thèse porte sur l'inférence de réseaux. Le cadre statistique naturel à ce genre de problèmes est celui des modèles graphiques, dans lesquels les relations de dépendance et d'indépendance conditionnelles vérifiées par une distribution multivariée sont représentées à l'aide d'un graphe. Il s'agit alors d'apprendre la structure du modèle à partir d'observations portant sur les sommets. Nous considérons le problème d'un point de vue bayésien. Nous avons également décidé de nous concentrer sur un sous-ensemble de graphes permettant d'effectuer l'inférence de manière exacte et efficace, à savoir celui des arbres couvrants. Il est en effet possible d'intégrer une fonction définie sur les arbres couvrants en un temps cubique par rapport au nombre de variables à la condition que cette fonction factorise selon les arêtes, et ce malgré le cardinal super-exponentiel de cet ensemble. En choisissant les distributions a priori sur la structure et les paramètres du modèle de manière appropriée, il est possible de tirer parti de ce résultat pour l'inférence de modèles graphiques arborescents. Nous proposons un cadre formel complet pour cette approche.Nous nous intéressons également au cas où les observations sont organisées en série temporelle. En faisant l'hypothèse que la structure du modèle graphique latent subit un certain nombre de brusques changements, le but est alors de retrouver le nombre et la position de ces points de rupture. Il s'agit donc d'un problème de segmentation. Sous certaines hypothèses de factorisation, l'exploration exhaustive de l'ensemble des segmentations est permise et, combinée aux résultats sur les arbres couvrants, permet d'obtenir, entre autres, la distribution a posteriori des points de ruptures en un temps polynomial à la fois par rapport au nombre de variables et à la longueur de la série. / In this dissertation we investigate the problem of network inference. The statistical frame- work tailored to this task is that of graphical models, in which the (in)dependence relation- ships satis ed by a multivariate distribution are represented through a graph. We consider the problem from a Bayesian perspective and focus on a subset of graphs making structure inference possible in an exact and e cient manner, namely spanning trees. Indeed, the integration of a function de ned on spanning trees can be performed with cubic complexity with respect to number of variables under some factorisation assumption on the edges, in spite of the super-exponential cardinality of this set. A careful choice of prior distributions on both graphs and distribution parameters allows to use this result for network inference in tree-structured graphical models, for which we provide a complete and formal framework.We also consider the situation in which observations are organised in a multivariate time- series. We assume that the underlying graph describing the dependence structure of the distribution is a ected by an unknown number of abrupt changes throughout time. Our goal is then to retrieve the number and locations of these change-points, therefore dealing with a segmentation problem. Using spanning trees and assuming that segments are inde- pendent from one another, we show that this can be achieved with polynomial complexity with respect to both the number of variables and the length of the series.

Le travail que nous développons dans le cadre de cette thèse s'articule autour des problèmes de recherche de structure de recouvrement de graphes sous contrainte sur le degré des sommets. Comme l'arbre de recouvrement couvre les sommets d'un graphe connexe avec un minimum de liens, il est généralement proposé comme solution à ce type de problèmes. Cependant, pour certaines applications telles que le routage dans les réseaux optiques, les solutions ne sont pas nécessairement des sous-graphes. Nous supposons dans cette thèse que la contrainte sur le degré est due à une capacité limitée instantanée des sommets et que la seule exigence sur le recouvrement est sa connexité. Dans ce cas, la solution peut être différente d'un arbre. Nous reformulons ces problèmes de recouvrement en nous appuyant sur une extension du concept d'arbre appelée hiérarchie de recouvrement. Notre objectif principal est de démontrer son intérêt vis-à-vis de l'arbre en termes de faisabilité et de coût du recouvrement. Nous considérons deux types de contraintes sur le degré : des bornes sur le degré des sommets ou une borne sur le nombre de sommets de branchement et cherchons dans les deux cas un recouvrement de coût minimum. Nous illustrons aussi l'applicabilité des hiérarchies en étudiant un problème prenant davantage en compte la réalité du routage optique. Pour ces différents problèmes NP-difficiles, nous montrons, tant sur le coût des solutions optimales que sur la garantie de performance des solutions approchées, l'intérêt des hiérarchies de recouvrement. Ce constat se voit conforté par des expérimentations sur des graphes aléatoires. / The work conducted in this thesis is focused on the minimum spanning problems in graphs under constraints on the vertex degrees. As the spanning tree covers the vertices of a connected graph with a minimum number of links, it is generally proposed as a solution for this kind of problems. However, for some applications such as the routing in optical networks, the solution is not necessarily a sub-graph. In this thesis, we assume that the degree constraints are due to a limited instantaneous capacity of the vertices and that the only pertinent requirement on the spanning structure is its connectivity. In that case, the solution may be different from a tree. We propose the reformulation of this kind of spanning problems. To find the optimal coverage of the vertices, an extension of the tree concept called hierarchy is proposed. Our main purpose is to show its interest regarding the tree in term of feasibility and costs of the coverage. Thus, we take into account two types of degree constraints: either an upper bound on the degree of vertices and an upper bound on the number of branching vertices. We search a minimum cost spanning hierarchy in both cases. Besides, we also illustrate the applicability of hierarchies by studying a problem that takes more into account the reality of the optical routing. For all those NP-hard problems, we show the interest of the spanning hierarchy for both costs of optimal solutions and performance guarantee of approximate solutions. These results are confirmed by several experimentations on random graphs.

Dans cette thèse, nous proposons des solutions parrallèles basées sur le systèmes actuel GPU (graphics processing unit) pour deux problèmes de minimisation de graphe Euclidien, à savoir le problème de forêt/arbre couvrant minimum Euclidien (EMSF / EMST) et le problème du voyageur commerce (TSP). Les solutions proposées résolvent également aussi le problème d'une paire bichromatique la plus proche (BCP), et suivent la technique de ``contrôle décentralisé, du parallélisme des données et des mémoires partagées par GPU".Nous proposons une technique de recherche dans le voisinage le plus proche de dimension K Euclidienne basée sur les approches classiques de NNS d’Elias qui divisent l’espace Euclidien en cellules congruentes et ne se chevauchant pas, où la taille des points de chaque cellule est délimitée. Nous proposons aussi une technique d'élagage pour obtenir le NNS à base de composants afin de trouver le point de sortie le plus proche de l'ensemble de points de requête de Q dans la complexité temporelle linéaire séquentielle lorsque les données sont uniformément réparties. Ces techniques sont utilisées conjointement avec deux GPU algorithmes proposés pour arbre traversement, à savoir la recherche en largeur bidirectionnelle GPU et la liste chaînée dynamique distribuée, afin d'adresser le BCP. Basé sur la solution BCP, un algorithme parallèle Divide and Conquer est implémenté pour construire EMSF et EMST totalement côté GPU. Le TSP est adressé avec différents algorithmes de recherche locaux parallèles 2-opt, dans lesquels nous proposons une méthodologie ``évaluation multiple K-opt, mouvements multiples K-opt" afin d’exécuter simultanément, sans interférence, des processus massifs 2-/3-opt mouvements qui se retrouvent globalement sur le même circuit TSP pour de nombreux bords. Cette méthodologie est expliquée en détail pour montrer comment nous obtenons un calcul haute performance à la fois du côté du GPU et CPU. Nous testons les solutions proposées et rapportons des résultats de comparaison expérimentale par rapport aux algorithmes de pointe. / In this thesis, we propose parallel solutions based on current graphics processing unit (GPU) system for two Euclidean graph minimization problems, namely the Euclidean minimum spanning forest/tree (EMSF/EMST) and the travelling salesman problem (TSP). The proposed solutions also solve the bichromatic closest pair (BCP) problem, and follow technique of ``decentralized control, data parallelism, GPU shared memories".We propose a Euclidean K-dimensional nearest neighbourhood search (NNS) technique based on classical Elias' NNS approaches that divide the Euclidean space into congruent and non-overlapping cells where size of points in each cell is bounded. We propose a pruning technique to obtain component-based NNS to find a query point set Q's closest outgoing point within sequential linear time complexity when the data is uniformly distributed. These techniques are used together with two proposed GPU tree traversal algorithms, namely the GPU two-direction Breadth-first search and distributed dynamic linked list, to address the BCP. Based on the BCP solution, a divide and conquer parallel algorithm is implemented for building EMSF and EMST totally on GPU side. The TSP is addressed with different parallel 2-opt local search algorithms, in which we propose a ``multiple K-opt evaluation, multiple K-opt moves" methodology in order to simultaneously execute, without interference, massive 2-/3-opt moves that are globally found on the same TSP tour for many edges. This methodology is explained in details to show how we obtain high performance computing both on GPU and CPU side. We test the proposed solutions and report experimental comparison results against the state-of-the-art algorithms.