Tratamos da generalização do problema da geração de caminho mínimo, no qual não apenas um, mas vários caminhos de menores custos devem ser produzidos. O problema dos k-menores caminhos consiste em listar os k caminhos de menores custos conectando um par de vértices. Esta dissertação trata de algoritmos para geração de k-menores caminhos em grafos simétricos com custos não-negativos, bem como algumas implementações destes. / We consider a long-studied generalization of the shortest path problem, in which not one but several short paths must be produced. The k-shortest (simple) paths problem is to list the k paths connecting a given source-destination pair in the digraph with minimum total length. This dissertation deals with k-shortest simple paths algorithms designed for nonnegative costs, undirected graphs and some implementations of them.

Tratamos da generalização do problema da geração de caminho mínimo, no qual não apenas um, mas vários caminhos de menores custos devem ser produzidos. O problema dos k-menores caminhos consiste em listar os k caminhos de menores custos conectando um par de vértices. Esta dissertação trata de algoritmos para geração de k-menores caminhos em grafos simétricos com custos não-negativos, bem como algumas implementações destes. / We consider a long-studied generalization of the shortest path problem, in which not one but several short paths must be produced. The k-shortest (simple) paths problem is to list the k paths connecting a given source-destination pair in the digraph with minimum total length. This dissertation deals with k-shortest simple paths algorithms designed for nonnegative costs, undirected graphs and some implementations of them.

Signaling pathways are widely studied in systems biology. Several databases catalog our knowledge of these pathways, including the proteins and interactions that comprise them. However, high-quality curation of this information is slow and painstaking. As a result, many interactions still lack annotation concerning the pathways they participate in. A natural question that arises is whether or not it is possible to automatically leverage existing annotations to identify new interactions for inclusion in a given pathway. Here, we present RegLinker, an algorithm that achieves this purpose by computing multiple short paths from pathway receptors to transcription factors (TFs) within a background interaction network. The key idea underlying RegLinker is the use of regular-language constraints to control the number of non-pathway edges present in the computed paths. We systematically evaluate RegLinker and alternative approaches against a comprehensive set of 15 signaling pathways and demonstrate that RegLinker exhibits superior recovery of withheld pathway proteins and interactions. These results show the promise of our approach for prioritizing candidates for experimental study and the broader potential of automated analysis to attenuate difficulties of traditional manual inquiry. / Master of Science / Cells in the human body are constantly receiving signals that inform their response to a variety of conditions. These signals serve as cues to a cell, allowing it to make informed decisions that impact cellular processes such as movement, growth, and death. Cells employ proteins and the interactions between them to achieve these capabilities. Signals manifest as molecules that interact with proteins bound to membrane of a cell. When this happens, a cascade of interactions between the proteins inside the cell will be set off. Ultimately, this cascade activate or inhibit the cell’s production of new proteins, constituting a response to the signal received. The proteins and interactions involved in such a cascade together form what is known as a signaling pathway. Experiments have uncovered the interactions that are present in many signaling pathways, and researchers have carefully cataloged this information in publicly available databases. However, high-quality curation is slow and painstaking, and many known interactions have not been annotated as belonging to any pathway. A natural question that arises is whether or not it is possible to leverage existing annotations to automatically determine which new interactions to include in a given pathway. In this thesis, we present an efficient algorithm, RegLinker, for this purpose. We evaluate this method and alternative approaches on a comprehensive set of 15 signaling pathways and demonstrate that RegLinker is better at recovering interactions withheld from these pathways. In particular, we show RegLinker’s superior ability to identify interactions that utilize proteins that were not previously considered part of a pathway. These results underscore the promise of our approach for prioritizing candidates for experimental study and the broader potential of automated analysis to attenuate difficulties of traditional manual inquiry.

We study a specialized version of network design problems that arise in telecommunication, transportation and other industries. The problem, a generalization of the shortest path problem, is defined on an undirected network consisting of a set of arcs on which we can install (load), at a cost, a choice of up to three types of capacitated facilities. Our objective is to determine the configuration of facilities to load on each arc that will satisfy the demand of a single commodity at the lowest possible cost. Our results (i) demonstrate that the single-facility loading problem and certain "common breakeven point" versions of the two-facility and three-facility loading problems are polynomially solvable as a shortest path problem; (ii) show that versions of the twofacility loading problem are strongly NP-hard, but that a shortest path solution provides an asymptotically "good" heuristic; and (iii) characterize the optimal solution (that is, specify a linear programming formulation with integer solutions) of the common breakeven point versions of the two-facility and three-facility loading problems. In this development, we introduce two new families of facets, give geometric interpretations of our results, and demonstrate the usefulness of partitioning the space of the problem parameters to establish polyhedral integrality properties. Generalizations of our results apply to (i) multicommodity applications and (ii) situations with more than three facilities.

We provide a formal mathematical definition of the Shortest Paths for All Flows (SP-AF) problem and provide many efficient algorithms. The SP-AF problem combines the well known Shortest Paths (SP) and Bottleneck Paths (BP) problems, and can be solved by utilising matrix multiplication. Thus in our research of the SP-AF problem, we also make a series of contributions to the underlying topics of the SP problem, the BP problem, and matrix multiplication. For the topic of matrix multiplication we show that on an n-by-n two dimensional (2D) square mesh array, two n-by-n matrices can be multiplied in exactly 1.5n ‒ 1 communication steps. This halves the number of communication steps required by the well known Cannon’s algorithm that runs on the same sized mesh array. We provide two contributions for the SP problem. Firstly, we enhance the breakthrough algorithm by Alon, Galil and Margalit (AGM), which was the first algorithm to achieve a deeply sub-cubic time bound for solving the All Pairs Shortest Paths (APSP) problem on dense directed graphs. Our enhancement allows the algorithm by AGM to remain sub-cubic for larger upper bounds on integer edge costs. Secondly, we show that for graphs with n vertices, the APSP problem can be solved in exactly 3n ‒ 2 communication steps on an n-by-n 2D square mesh array. This improves on the previous result of 3.5n communication steps achieved by Takaoka and Umehara. For the BP problem, we show that we can compute the bottleneck of the entire graph without solving the All Pairs Bottleneck Paths (APBP) problem, resulting in a much more efficient time bound. Finally we define an algebraic structure called the distance/flow semi-ring to formally introduce the SP-AF problem, and we provide many algorithms for solving the Single Source SP-AF (SSSP-AF) problem and the All Pairs SP-AF (APSP-AF) problem. For the APSP-AF problem, algebraic algorithms are given that utilise faster matrix multiplication over a ring.

A classic problem Computational Geometry is finding all euclidean shortest paths in a simple polygon from a given source vertex to every other vertex in the boundary. In this text, we give a detailed description of the Visibility Graph and Shortest Path Tree structures that solve this problem and also present the Shortest Path Map structure that extends the solution to shortest paths to every point inside the polygon. / Um problema clássico em Geometria Computacional é: encontrar todos os caminhos mínimos euclidianos dentro de um polígono simples a partir de um dado vértice fonte para todos os outros vértices da borda. Neste texto, apresentamos detalhadamente as estruturas de Grafo de Visibilidade e Árvore de Caminhos Mínimos que resolvem este problema e descrevemos também a estrutura Mapa de Caminhos Mínimos que estende a solução para todos os pontos contidos dentro do polígono.

The ongoing development of new and demanding Internet applications requires the Internet to deliver better service levels that are significantly better than the best effort service that the Internet currently provides and was built for. These improved service levels include guaranteed delays, jitter and bandwidth. Through extensive research into Quality of Service and Differentiated Service (DiffServ) it has become possible to provide guaranteed services, however this turns out to be inadequate without the application of Traffic Engineering methodologies and principles. Traffic Engineering is an integral part of network operation. Its major goal is to deliver the best performance from an existing service provider's network resources and, at the same time, to enhance a customers' view of network performance. In this thesis, several different traffic engineering methods for optimising the operation of native IP and IP networks employing MPLS are proposed. A feature of these new methods is their fast run times and this opens the way to making them suitable for application in an online traffic engineering environment. For native IP networks running shortest path based routing protocols, we show that an LP-based optimisation based on the well known multi-commodity flow problem can be effective in removing network congestion. Having realised that Internet service providers are now moving towards migrating their networks to the use of MPLS, we have also formulated optimisation methods to traffic engineer MPLS networks by selecting suitable routing paths and utilising the feature of explicit routing contained in MPLS. Although MPLS is capable of delivering traffic engineering across different classes of traffic, network operators still prefer to rely on the proven and simple IP based routing protocols for best effort traffic and only use MPLS to route traffic requiring special forwarding treatment. Based on this fact, we propose a method that optimises the routing patterns applicable to different classes of traffic based on their bandwidth requirements. A traffic engineering comparison study that evaluates the performance of a neural network-based method for MPLS networks and LP-based weight setting approach for shortest path based networks has been performed using a well-known open source network simulator, called ns2. The comparative evaluation is based upon the packet loss probability. The final chapter of the thesis describes the software development of a network management application called OptiFlow which integrates techniques described in earlier chapters including the LP-based weight setting optimisation methodology; it also uses traffic matrix estimation techniques that are required as input to the weight setting models that have been devised. The motivation for developing OptiFlow was to provide a prototype set of tools that meet the congestion management needs of networking industries (ISPs and telecommunications companies - telcos).

In this thesis, an adaptive transit routing (ATR) problem in a schedule based stochastic time-dependent transit network is defined and formulated as a finite horizon Markov Decision Process (MDP). The transit link travel times are assumed to be random with known probability distributions. Routing strategies are defined to be conditional on the arrival times at intermediate nodes, and the location and arrival times of other buses in the network. In other words, a traveler in the network decides to walk, wait or board a bus based on the real time information of all buses in the network. The objective is to find a strategy that minimizes the expected travel time, subject to constraints that guarantee that the destination is reached within a certain threshold. The value of the threshold was chosen to reflect the risk averse attitude of travelers and is computed based on the earliest time by which the destination can be reached with probability 1. The problem inherits the curse of dimensionality and state space reduction through pre-processing is achieved by solving variants of the time dependent shortest path problem. An interesting analogy between the state space reduction techniques and the concept of light cones is discussed. A dynamic program framework to solve the problem is developed by defining the state space, decision space and transition functions. Numerical results on a small instance of the Austin transit network are presented to investigate the extent of reduction in state space using the proposed methods. / text

Real time information about traffic conditions is becoming widely available through various media, and the focus on Advanced Traveler Information Systems (ATIS) is gaining importance rapidly. In such conditions, travelers have better knowledge about the system and adapt as the system evolves dynamically during their travel. Drivers may change routes along their travel in order to optimize their own objective of travel, which can be characterized by disutility functions. The focus of this research is to study the behavior of travelers with multiple trip objectives, when provided with real time information. A web based experiment is carried out to simulate a traffic network with information provision and different travel objectives. The decision strategies of participants are analyzed and compared to the optimal policy, along with few other possible decision rules and a general model is calibrated to describe the travelers' decision strategy. This research is a step towards calibrating equilibrium models for adaptive behavior with multiple user classes. / text

A busca de soluções para a mobilidade urbana que minimizem a agressão do setor de tráfego e transportes ao meio ambiente está cada vez maior. Os veículos elétricos se posicionam como uma alternativa interessante, pois reduzem a emissão de gases poluentes na atmosfera, a poluição sonora e o consumo de petróleo. No entanto, sua limitada autonomia e a escassez de postos de recarga intimidam sua adoção. Por conta disso, políticas governamentais de incentivo têm sido desenvolvidas para a oferta de benefícios a quem optar por um veículo elétrico. Estima-se que dentro de poucas décadas toda a frota urbana será substituída por veículos dessa natureza. Por isso, é importante entender as mudanças no tempo de viagem e no consumo de energia oriundos da inclusão de veículos elétricos em cenários de tráfego. Trabalhos anteriores estudaram as diferenças entre os mecanismos internos de veículos convencionais e elétricos na determinação destas mudanças. Porém, dadas as características destes últimos, motoristas de veículos elétricos se preocupam com a economia de energia e podem optar por rotas diferentes. Logo, uma análise completa destes impactos deve considerar uma nova distribuição de tráfego. Este trabalho propõe um método biobjetivo de alocação de tráfego que considera o tempo de viagem e o consumo de energia para determinar a distribuição de veículos elétricos em cenários de tráfego urbano. Duas estratégias de distribuição de fluxo são propostas como mecanismos de escolha de rotas. Como parte da alocação de tráfego, é proposto um algoritmo biobjetivo de caminhos mínimos para veículos elétricos. A abordagem apresentada foi aplicada a três cenários distintos, onde percebeu-se uma diminuição de até 80% no consumo total de energia. Em cenários com congestionamento, observou-se um aumento de 10% no tempo de viagem. Já em cenários sem congestionamento o tempo de viagem diminuiu cerca de 2%. A recuperação de energia representa quase 6% da economia total dos veículos elétricos. Além disso, experimentos mostraram que investimentos na eficiência dos veículos elétricos podem resultar em uma economia de até 15% de energia. / The search for urban mobility solutions that minimize the aggression to the environment is increasing. Electric vehicles are an attractive alternative because they reduce greenhouse gas emissions, noise pollution, and oil consumption. However, their limited autonomy and the lack of charging stations restrict their popularization. Therefore, government incentive policies have been developed in order to offer benefits to those who choose an electric vehicle. It is estimated that the entire urban fleet will be replaced by these vehicles in a few decades. Therefore, it is important to understand the changes in travel time and energy consumption from the inclusion of electric vehicles in traffic scenarios. Previous works determined these changes by studying the differences between the internal engine of conventional and electric vehicles. However, given the characteristics of the latter, drivers of electric vehicles care about saving energy and may want to choose different routes. Thus, a complete analysis of these impacts should consider a redistribution of traffic. This work proposes a bi-objective traffic assignment method that considers the travel time and the energy consumption to determine the distribution of electric vehicles in urban traffic scenarios. We introduce two strategies for flow distribution as models of route choice. As a procedure of the traffic assignment method, we propose a bi-objective shortest path algorithm for electric vehicles. Our approach was applied to three different scenarios, which resulted in a decrease of up to 80% in total energy consumption. In congested scenarios, we observe an increase of about 10% in average travel time. In uncongested scenarios, travel time decreases about 2%. Energy recovery is almost 6% of the total savings of electric vehicles. Moreover, experiments have shown that investments in the efficiency of electric vehicles can result in up to 15% of energy savings.