Properties and Algorithms of the KCube Interconnection Networks

The KCube interconnection network was first introduced in 2010 in order to exploit the good characteristics of two well-known interconnection networks, the hypercube and the Kautz graph. KCube links up multiple processors in a communication network with high density for a fixed degree. Since the KCube network is newly proposed, much study is required to demonstrate its potential properties and algorithms that can be designed to solve parallel computation problems. In this thesis we introduce a new methodology to construct the KCube graph. Also, with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k). Moreover, we will find its connectivity followed by an optimal broadcasting scheme in which a source node containing a message is to communicate it with all other processors. In addition to KCube networks, we have studied a version of the routing problem in the traditional hypercube, investigating this problem: whether there exists a shortest path in a Qn between two nodes 0n and 1n, when the network is experiencing failed components. We first conditionally discuss this problem when there is a constraint on the number of faulty nodes, and subsequently introduce an algorithm to tackle the problem without restrictions on the number of nodes.

Méthodes exactes et heuristiques pour le problème de tournées de véhicules avec fenêtres de temps et réutilisation de véhicules

Cette thèse porte sur les problèmes de tournées de véhicules avec fenêtres de temps où un gain est associé à chaque client et où l'objectif est de maximiser la somme des gains recueillis moins les coûts de transport. De plus, un même véhicule peut effectuer plusieurs tournées durant l'horizon de planification. Ce problème a été relativement peu étudié en dépit de son importance en pratique. Par exemple, dans le domaine de la livraison de denrées périssables, plusieurs tournées de courte durée doivent être combinées afin de former des journées complètes de travail. Nous croyons que ce type de problème aura une importance de plus en plus grande dans le futur avec l'avènement du commerce électronique, comme les épiceries électroniques, où les clients peuvent commander des produits par internet pour la livraison à domicile. Dans le premier chapitre de cette thèse, nous présentons d'abord une revue de la littérature consacrée aux problèmes de tournées de véhicules avec gains ainsi qu'aux problèmes permettant une réutilisation des véhicules. Nous présentons les méthodologies générales adoptées pour les résoudre, soit les méthodes exactes, les méthodes heuristiques et les méta-heuristiques. Nous discutons enfin des problèmes de tournées dynamiques où certaines données sur le problème ne sont pas connues à l'avance. Dans le second chapitre, nous décrivons un algorithme exact pour résoudre un problème de tournées avec fenêtres de temps et réutilisation de véhicules où l'objectif premier est de maximiser le nombre de clients desservis. Pour ce faire, le problème est modélisé comme un problème de tournées avec gains. L'algorithme exact est basé sur une méthode de génération de colonnes couplée avec un algorithme de plus court chemin élémentaire avec contraintes de ressources. Pour résoudre des instances de taille réaliste dans des temps de calcul raisonnables, une approche de résolution de nature heuristique est requise. Le troisième chapitre propose donc une méthode de recherche adaptative à grand voisinage qui exploite les différents niveaux hiérarchiques du problème (soit les journées complètes de travail des véhicules, les routes qui composent ces journées et les clients qui composent les routes). Dans le quatrième chapitre, qui traite du cas dynamique, une stratégie d'acceptation et de refus des nouvelles requêtes de service est proposée, basée sur une anticipation des requêtes à venir. L'approche repose sur la génération de scénarios pour différentes réalisations possibles des requêtes futures. Le coût d'opportunité de servir une nouvelle requête est basé sur une évaluation des scénarios avec et sans cette nouvelle requête. Enfin, le dernier chapitre résume les contributions de cette thèse et propose quelques avenues de recherche future.

Tactical Vehicle Routing Planning with Application to Milk Collection and Distribution

De nombreux problèmes pratiques qui se posent dans dans le domaine de la logistique, peuvent être modélisés comme des problèmes de tournées de véhicules. De façon générale, cette famille de problèmes implique la conception de routes, débutant et se terminant à un dépôt, qui sont utilisées pour distribuer des biens à un nombre de clients géographiquement dispersé dans un contexte où les coûts associés aux routes sont minimisés. Selon le type de problème, un ou plusieurs dépôts peuvent-être présents. Les problèmes de tournées de véhicules sont parmi les problèmes combinatoires les plus difficiles à résoudre. Dans cette thèse, nous étudions un problème d’optimisation combinatoire, appartenant aux classes des problèmes de tournées de véhicules, qui est liée au contexte des réseaux de transport. Nous introduisons un nouveau problème qui est principalement inspiré des activités de collecte de lait des fermes de production, et de la redistribution du produit collecté aux usines de transformation, pour la province de Québec. Deux variantes de ce problème sont considérées. La première, vise la conception d’un plan tactique de routage pour le problème de la collecte-redistribution de lait sur un horizon donné, en supposant que le niveau de la production au cours de l’horizon est fixé. La deuxième variante, vise à fournir un plan plus précis en tenant compte de la variation potentielle de niveau de production pouvant survenir au cours de l’horizon considéré. Dans la première partie de cette thèse, nous décrivons un algorithme exact pour la première variante du problème qui se caractérise par la présence de fenêtres de temps, plusieurs dépôts, et une flotte hétérogène de véhicules, et dont l’objectif est de minimiser le coût de routage. À cette fin, le problème est modélisé comme un problème multi-attributs de tournées de véhicules. L’algorithme exact est basé sur la génération de colonnes impliquant un algorithme de plus court chemin élémentaire avec contraintes de ressources. Dans la deuxième partie, nous concevons un algorithme exact pour résoudre la deuxième variante du problème. À cette fin, le problème est modélisé comme un problème de tournées de véhicules multi-périodes prenant en compte explicitement les variations potentielles du niveau de production sur un horizon donné. De nouvelles stratégies sont proposées pour résoudre le problème de plus court chemin élémentaire avec contraintes de ressources, impliquant dans ce cas une structure particulière étant donné la caractéristique multi-périodes du problème général. Pour résoudre des instances de taille réaliste dans des temps de calcul raisonnables, une approche de résolution de nature heuristique est requise. La troisième partie propose un algorithme de recherche adaptative à grands voisinages où de nombreuses nouvelles stratégies d’exploration et d’exploitation sont proposées pour améliorer la performances de l’algorithme proposé en termes de la qualité de la solution obtenue et du temps de calcul nécessaire.

Safe Distributed Coordination of Heterogeneous Robots through Dynamic Simple Temporal Networks

Research on autonomous intelligent systems has focused on how robots can robustly carry out missions in uncertain and harsh environments with very little or no human intervention. Robotic execution languages such as RAPs, ESL, and TDL improve robustness by managing functionally redundant procedures for achieving goals. The model-based programming approach extends this by guaranteeing correctness of execution through pre-planning of non-deterministic timed threads of activities. Executing model-based programs effectively on distributed autonomous platforms requires distributing this pre-planning process. This thesis presents a distributed planner for modelbased programs whose planning and execution is distributed among agents with widely varying levels of processor power and memory resources. We make two key contributions. First, we reformulate a model-based program, which describes cooperative activities, into a hierarchical dynamic simple temporal network. This enables efficient distributed coordination of robots and supports deployment on heterogeneous robots. Second, we introduce a distributed temporal planner, called DTP, which solves hierarchical dynamic simple temporal networks with the assistance of the distributed Bellman-Ford shortest path algorithm. The implementation of DTP has been demonstrated successfully on a wide range of randomly generated examples and on a pursuer-evader challenge problem in simulation.

Visibility and proximity on triangulated surfaces

En aquesta tesi es solucionen problemes de visibilitat i proximitat sobre superfícies triangulades considerant elements generalitzats. Com a elements generalitzats considerem: punts, segments, poligonals i polígons. Les estrategies que proposem utilitzen algoritmes de geometria computacional i hardware gràfic. Comencem tractant els problemes de visibilitat sobre models de terrenys triangulats considerant un conjunt d'elements de visió generalitzats. Es presenten dos mètodes per obtenir, de forma aproximada, mapes de multi-visibilitat. Un mapa de multi-visibilitat és la subdivisió del domini del terreny que codifica la visibilitat d'acord amb diferents criteris. El primer mètode, de difícil implementació, utilitza informació de visibilitat exacte per reconstruir de forma aproximada el mapa de multi-visibilitat. El segon, que va acompanyat de resultats d'implementació, obté informació de visibilitat aproximada per calcular i visualitzar mapes de multi-visibilitat discrets mitjançant hardware gràfic. Com a aplicacions es resolen problemes de multi-visibilitat entre regions i es responen preguntes sobre la multi-visibilitat d'un punt o d'una regió. A continuació tractem els problemes de proximitat sobre superfícies polièdriques triangulades considerant seus generalitzades. Es presenten dos mètodes, amb resultats d'implementació, per calcular distàncies des de seus generalitzades sobre superfícies polièdriques on hi poden haver obstacles generalitzats. El primer mètode calcula, de forma exacte, les distàncies definides pels camins més curts des de les seus als punts del poliedre. El segon mètode calcula, de forma aproximada, distàncies considerant els camins més curts sobre superfícies polièdriques amb pesos. Com a aplicacions, es calculen diagrames de Voronoi d'ordre k, i es resolen, de forma aproximada, alguns problemes de localització de serveis. També es proporciona un estudi teòric sobre la complexitat dels diagrames de Voronoi d'ordre k d'un conjunt de seus generalitzades en un poliedre sense pesos.

Production and Delivery (Optimization of production system and reliability)

This thesis is done to solve two issues for Sayid Paper Mill Ltd Pakistan. Section one deals with a practical problem arise in SPM that is cutting a given set of raw paper rolls of known length and width, and a set of product paper rolls of known length (equal to the length of raw paper rolls) and width, practical cutting constraints on a single cutting machine, according to demand orders for all customers. To solve this problem requires to determine an optimal cutting schedule to maximize the overall cutting process profitability while satisfying all demands and cutting constraints. The aim of this part of thesis is to develop a mathematical model which solves this problem.Second section deals with a problem of delivering final product from warehouse to different destinations by finding shortest paths. It is an operational routing problem to decide the daily routes for sending trucks to different destination to deliver their final product. This industrial problem is difficult and includes aspect such as delivery to a single destination and multiple destinations with limited resources. The aim of this part of thesis is to develop a process which helps finding shortest path.

Avaliação de desempenho de algoritmos de alocação de comprimento de onda em redes ópticas WDM

Neste trabalho estudamos alguns algoritmos de alocação de comprimento de onda em redes ópticas WDM (Wavelength Division Multiplexing). O objetivo para estudar os algoritmos de alocação first-fit, least-used e most-used está baseado na estratégia adotada para estudar o Problema RWA. A estratégia toma como base a visão geral do problema que envolve os algoritmos de roteamento e os algoritmos de alocação de comprimento de onda, e tendo como métrica principal para seus resultados a probabilidade de bloqueio. Este trabalho apresenta uma visão diferenciada para o problema e considera-se que a alocação de comprimentos de onda se sobrepõe, em importância, à ação de roteamento em redes ópticas. Essa percepção ocorre quando se analisa o problema RWA a partir do critério clássico usado no estabelecimento de uma rota: a escolha do caminho mais curto entre a origem e o destino. Apesar da identificação de um caminho mais curto, isso não garante, em redes ópticas, que ele será o utilizado, pois é necessário que haja para aquele caminho, um comprimento de onda adequado. Foi utilizada uma ferramenta de simulação para redes WDM denominada OWNS para realizar uma análise do problema RWA. Os resultados obtidos são apresentados graficamente e em uma das simulações observou-se uma forte tendência de queda na probabilidade de bloqueio e uma boa vazão no trafego da rede com isso possibilitando um aumento na capacidade de transmissão da rede. Por fim, este texto apresenta uma discussão sobre os diferenciais e limitações deste trabalho, e apresenta direcionamentos para investigações futuras neste campo de estudo.

Wavelength assignment using a hybrid evolutionary computation to reduce cross-phase modulation

In this paper, we propose a hybrid methodology based on Graph-Coloring and Genetic Algorithm (GA) to solve the Wavelength Assignment (WA) problem in optical networks, impaired by physical layer effects. Our proposal was developed for a static scenario where the physical topology and traffic matrix are known a priori. First, we used fixed shortest-path routing to attend demand requests over the physical topology and the graph-coloring algorithm to minimize the number of necessary wavelengths. Then, we applied the genetic algorithm to solve WA. The GA finds the wavelength activation order on the wavelengths grid with the aim of reducing the Cross-Phase Modulation (XPM) effect; the variance due to the XPM was used as a function of fitness to evaluate the feasibility of the selected WA solution. Its performance is compared with the First-Fit algorithm in two different scenarios, and has shown a reduction in blocking probability up to 37.14% when considered both XPM and residual dispersion effects and up to 71.42% when only considered XPM effect. Moreover, it was possible to reduce by 57.14% the number of wavelengths.

Performance Analysis of Sparse Traffic Grooming in WDM Mesh Networks

Sparse traffic grooming is a practical problem to be addressed in heterogeneous multi-vendor optical WDM networks where only some of the optical cross-connects (OXCs) have grooming capabilities. Such a network is called as a sparse grooming network. The sparse grooming problem under dynamic traffic in optical WDM mesh networks is a relatively unexplored problem. In this work, we propose the maximize-lightpath-sharing multi-hop (MLS-MH) grooming algorithm to support dynamic traffic grooming in sparse grooming networks. We also present an analytical model to evaluate the blocking performance of the MLS-MH algorithm. Simulation results show that MLSMH outperforms an existing grooming algorithm, the shortest path single-hop (SPSH) algorithm. The numerical results from analysis show that it matches closely with the simulation. The effect of the number of grooming nodes in the network on the blocking performance is also analyzed.

Zonificación del espacio por agrupación de unidades superficiales. Aplicación a la gestión de sistemas extensivos del tipo cereal-ovino

RESUMEN Los procesos de diseño de zonas o diseño del territorio implican la partición de un espacio geográfico, organizado en un conjunto de unidades de área, en diferentes regiones o zonas según un conjunto especifico de criterios que varían en función del campo de aplicación. En la mayoría de los casos, el objetivo fundamental consiste en crear zonas de tamaño aproximadamente igual respecto a uno o varios atributos de medida -de carácter cuantitativo- (zonas con igual número de habitantes, igual promedio de ventas...). Sin embargo, están apareciendo nuevas aplicaciones, algunas en el contexto de las políticas de desarrollo sostenible, cuya finalidad es la definición de regiones con un tamaño predeterminado, no necesariamente similar. Además, en estos casos las zonas han de formarse en torno a un conjunto específico de posiciones, semillas o generadores. Este tipo de particiones no han sido lo suficientemente investigadas, de manera que no se conocen modelos de solución para la delimitación automática de las zonas. En esta tesis se ha diseñado un nuevo método basado en una versión discreta del diagrama de Voronoi con peso aditivo adaptativo (DVPAA), que permite la partición de un espacio bidimensional en zonas de un tamaño específico, considerando tanto la posición como el peso de cada uno de los generadores. El método consiste en resolver repetidamente un tradicional diagrama de Voronoi con peso aditivo, de forma que los pesos de cada generador se actualizan en cada iteración. En el proceso de cálculo de distancias se usa una métrica basada en el camino más corto, lo que garantiza que la partición obtenida esté formada por un conjunto de zonas conexas. La heurística diseñada se integra en una aplicación prototipo, desarrollada en un entorno SIG (Sistemas de Información Geográfica), que permite el trazado automático de zonas según los criterios anteriormente expuestos. Para analizar la viabilidad del método se ha utilizado como caso de estudio la gestión de los recursos pastorales para la ganadería extensiva en tres municipios de Castilla-La Mancha. Las pruebas realizadas ponen de manifiesto que la heurística diseñada, adaptada a los criterios que se plantean en el contexto de la gestión de sistemas extensivos agropecuarios, es válida para resolver este tipo de problemas de partición. El método propuesto se caracteriza por su eficacia en el tratamiento de un gran número de unidades superficiales en formato vectorial, generando soluciones que convergen con relativa rapidez y verifican los criterios establecidos. En el caso estudiado, aunque la posición prefijada de los generadores reduce considerablemente la complejidad del problema, existen algunas configuraciones espaciales de estos elementos para las que el algoritmo no encuentra una solución satisfactoria, poniéndose de manifiesto una de las limitaciones de este modelo. Tal y como se ha podido comprobar, la localización de los generadores puede tener un considerable impacto en la zonificación resultante, por lo que, de acuerdo con Kalcsics et al. (2005), una selección "inadecuada" difícilmente puede generar regiones válidas que verifiquen los criterios establecidos. ABSTRACT Tenitory or zone design processes entail partitioning a geographic space, organized as a set of basic areal units, into different regions or zones according to a specific set of entena that are dependent on the application context. In most cases the aim is to create zones that have approximately equal sizes with respect to one or several measure attributes (zones with equal numbers of inhabitants, same average sales, etc). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of positions, seeds or generators. This type of partitioning has not been sufñciently researched; therefore there are no known approaches for automated zone delimitation. This thesis proposes a new method based on a discrete versión of the Adaptive Additively Weighted Voronoi Diagram (AAWVD) that makes it possible to partition a 2D space into zones of specific sizes, taking both the position and the weight of each (seed) generator into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that the weights of each generator are updated at every iteration. The partition s zones are geographically connected nsing a metric based 011 the shortest path. The proposed heuristic lias been included in an application, developed in a GIS environment that allows the automated zone delimitation according to the mentioned criteria. The management of the extensive farming system of three municipalities of Castilla-La Mancha (Spain) has been used as study case to analyze the viability of the method. The tests carried out have established that the proposed method, adapted to the criteria of this application field, is valid for solving this type of partition problem. The applied algorithm is capable of handling a high number of vector areal units, generating solutions that converge in a reasonable CPU time and comply with the imposed constraints. Although the complexity of this problem is greatly reduced when the generator's positions are fixed, in many cases, these positions impose a spatial confignration that the algorithm proposed is unable to solve, thus revealing one of the limitations of this method. It has been shown that the location of the generators has a considerable impact on the final solution, so that, as Kalcsics et al. (2005) observed, an "inadequate" selection can hardly generate valid zones that comply with the established criteria.

Zone design of specific sizes using adaptive additively weighted voronoi diagrams

Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of seeds. This type of partitioning has not been sufficiently researched; therefore, there are no known approaches for automated zone delimitation. This study proposes a new method based on a discrete version of the adaptive additively weighted Voronoi diagram that makes it possible to partition a two-dimensional space into zones of specific sizes, taking both the position and the weight of each seed into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that each seed?s weight is updated at every iteration. The zones are geographically connected using a metric based on the shortest path. Tests conducted on the extensive farming system of three municipalities in Castile-La Mancha (Spain) have established that the proposed heuristic procedure is valid for solving this type of partitioning problem. Nevertheless, these tests confirmed that the given seed position determines the spatial configuration the method must solve and this may have a great impact on the resulting partition.

Quantum computation as geometry

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.

Surface k-NN query processing

A k-NN query finds the k nearest-neighbors of a given point from a point database. When it is sufficient to measure object distance using the Euclidian distance, the key to efficient k-NN query processing is to fetch and check the distances of a minimum number of points from the database. For many applications, such as vehicle movement along road networks or rover and animal movement along terrain surfaces, the distance is only meaningful when it is along a valid movement path. For this type of k-NN queries, the focus of efficient query processing is to minimize the cost of computing distances using the environment data (such as the road network data and the terrain data), which can be several orders of magnitude larger than that of the point data. Efficient processing of k-NN queries based on the Euclidian distance or the road network distance has been investigated extensively in the past. In this paper, we investigate the problem of surface k-NN query processing, where the distance is calculated from the shortest path along a terrain surface. This problem is very challenging, as the terrain data can be very large and the computational cost of finding shortest paths is very high. We propose an efficient solution based on multiresolution terrain models. Our approach eliminates the need of costly process of finding shortest paths by ranking objects using estimated lower and upper bounds of distance on multiresolution terrain models.

Unfolding kernel embeddings of graphs:enhancing class separation through manifold learning

In this paper, we investigate the use of manifold learning techniques to enhance the separation properties of standard graph kernels. The idea stems from the observation that when we perform multidimensional scaling on the distance matrices extracted from the kernels, the resulting data tends to be clustered along a curve that wraps around the embedding space, a behavior that suggests that long range distances are not estimated accurately, resulting in an increased curvature of the embedding space. Hence, we propose to use a number of manifold learning techniques to compute a low-dimensional embedding of the graphs in an attempt to unfold the embedding manifold, and increase the class separation. We perform an extensive experimental evaluation on a number of standard graph datasets using the shortest-path (Borgwardt and Kriegel, 2005), graphlet (Shervashidze et al., 2009), random walk (Kashima et al., 2003) and Weisfeiler-Lehman (Shervashidze et al., 2011) kernels. We observe the most significant improvement in the case of the graphlet kernel, which fits with the observation that neglecting the locational information of the substructures leads to a stronger curvature of the embedding manifold. On the other hand, the Weisfeiler-Lehman kernel partially mitigates the locality problem by using the node labels information, and thus does not clearly benefit from the manifold learning. Interestingly, our experiments also show that the unfolding of the space seems to reduce the performance gap between the examined kernels.

Algorithms for Geometric Matching, Clustering, and Covering

With the popularization of GPS-enabled devices such as mobile phones, location data are becoming available at an unprecedented scale. The locations may be collected from many different sources such as vehicles moving around a city, user check-ins in social networks, and geo-tagged micro-blogging photos or messages. Besides the longitude and latitude, each location record may also have a timestamp and additional information such as the name of the location. Time-ordered sequences of these locations form trajectories, which together contain useful high-level information about people's movement patterns.

The first part of this thesis focuses on a few geometric problems motivated by the matching and clustering of trajectories. We first give a new algorithm for computing a matching between a pair of curves under existing models such as dynamic time warping (DTW). The algorithm is more efficient than standard dynamic programming algorithms both theoretically and practically. We then propose a new matching model for trajectories that avoids the drawbacks of existing models. For trajectory clustering, we present an algorithm that computes clusters of subtrajectories, which correspond to common movement patterns. We also consider trajectories of check-ins, and propose a statistical generative model, which identifies check-in clusters as well as the transition patterns between the clusters.

The second part of the thesis considers the problem of covering shortest paths in a road network, motivated by an EV charging station placement problem. More specifically, a subset of vertices in the road network are selected to place charging stations so that every shortest path contains enough charging stations and can be traveled by an EV without draining the battery. We first introduce a general technique for the geometric set cover problem. This technique leads to near-linear-time approximation algorithms, which are the state-of-the-art algorithms for this problem in either running time or approximation ratio. We then use this technique to develop a near-linear-time algorithm for this

shortest-path cover problem.