Orientador: Zanoni Dias / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-21T23:02:27Z (GMT). No. of bitstreams: 1 Galvao_GustavoRodrigues_M.pdf: 1280667 bytes, checksum: 0809ad85a3b7f16ff5d7af5fc4124f0a (MD5) Previous issue date: 2012 / Resumo: Ao longo da evolução, mutações globais podem alterar a ordem dos genes de um genoma. Tais mutações são chamadas de eventos de rearranjo. Em Rearranjo de Genomas, estimamos a distância evolutiva entre dois genomas calculando-se a distância de rearranjo entre eles, que é o tamanho da menor sequência de eventos de rearranjo que transforma um genoma no outro. Representando genomas como permutações, nas quais os genes aparecem como elemento, à distância de rearranjo pode ser obtido resolvendo-se o problema combinatório de ordenar uma permutação utilizando o menor número de eventos de rearranjo. Este problema, que é referido como Problema da Ordenação por Rearranjo, varia de acordo com os tipos de eventos de rearranjo considerados. Nesta dissertação, focamos nosso estudo em dois tipos de eventos: reversões e transposições. Variações do Problema da Ordenação por Rearranjo que consideram esses eventos têm se mostrado difíceis de ser resolvida otimamente, por isso a maior parte dos algoritmos propostos - os quais denominamos genericamente por algoritmos de rearranjo de genomas - são aproximados e é esperado que os próximos avanços ocorram nesse sentido. Em razão disso, desenvolvemos uma ferramenta que avalia as respostas desses algoritmos. Para ilustrar sua aplicação, nós a utilizamos para avaliar as respostas de 16 algoritmos de rearranjo de genomas aproximados relativos a 6 variações do Problema da Ordenação por Rearranjo. Além da ferramenta, este trabalho traz outras contribuições. Desenvolvemos um algoritmo exato para calcular distâncias de rearranjo que é mais eficiente em termos de uso de memória do que qualquer outro algoritmo que encontramos na literatura. Apresentamos conjecturas que dizem respeito à forma como as distâncias de rearranjo se distribuem. Validamos conjecturas referentes ao diâmetro, que é o maior valor alcançável pela distância de rearranjo entre uma permutação qualquer e a identidade considerando-se todas as permutações com o mesmo número de elementos. Apresentamos demonstrações formais para o fator de aproximação de alguns dos algoritmos avaliados. Por fim, mostramos que os fatores de aproximação de 7 dos 16 algoritmos avaliados não podem ser melhorados, o que contradiz algumas hipóteses levantadas na literatura, e conjecturamos que os fatores de aproximação de outros 6 algoritmos também não possam / Abstract: During evolution, global mutations may modify the gene order in a genome and such mutations are called rearrangement events. In Genome Rearrangements, we estimate the evolutionary distance between two genomes by computing the rearrangement distance between them, which is the length of the shortest sequence of rearrangement events that transforms one genome into the other. Representing genomes as permutations, in which genes appear as elements, the rearrangement distance can be obtained by solving the combinatorial problem of sorting a permutation using a minimum number of rearrangement events. This problem is referred to as Rearrangement Sorting Problem and varies accordingly to the types of rearrangement events considered. In this dissertation, we focus on two types of rearrangement events: reversals and transpositions. Variants of Rearrangement Sorting Problem involving these events have been shown to be difficult to solve optimally, therefore most of the proposed algorithms - which we denominate generically as genome rearrangement algorithms - are approximations, which have been the expected direction to follow. For this reason, we developed a tool that evaluates the results of these algorithms. To illustrate its application, we used it to evaluate the results of 16 genome rearrangement algorithms regarding 6 variants of Rearrangement Sorting Problem. Besides this tool, we developed an exact algorithm for computing rearrangement distances that is more efficient in terms of memory than any algorithm we have found in literature. Additionally, we presented conjectures on how the rearrangement distance are distributed and validated them regarding their diameter, which is the greatest value that the rearrangement distance between a permutation and the identity can reach considering all permutations with the same number of elements. Moreover, we presented formal proofs on the approximation ratio of some of the evaluated algorithms and showed that the approximation ratio of 7 out of the 16 evaluated algorithms cannot be improved, which contradicts some hypothesis raised in literature. Lastly, we conjectured that the approximation ratio of another 6 algorithms also cannot be improved / Mestrado / Ciência da Computação / Mestre em Ciência da Computação

[pt] Neste trabalho, apresentamos algoritmos aproximativos para dois problemas de otimização em árvores. Na primeira parte, consideramos o Problema de Atribuição de k-Hotlinks. Seja G= (V,E) um grafo direcionado acíclico representando um web site, onde nós correspondem a páginas e arcos correspondem a hyperlinks. Nesse contexto, hotlink são definidos como atalhos (novos arcos) adicionados às páginas de G de modo a reduzir o tempo gasto pelos usuários para alcançarem as informações desejadas. Neste trabalho consideramos o problema onde G é uma árvore enraizada e o objetivo é minimizar o tempo médio gasto pelos usuários atribuindo no máximo k hotlinks a cada nó. Para a versão mais estudada desse problema onde no máximo um hotlink pode ser atribuído a cada nó, provamos a existência de um FPTAS. Isso representa uma significante melhora em relação ao algoritmo com aproximação constante obtido recentemente em [Jacobs, WADS 2007]. Além disso, desenvolvemos o primeiro algoritmo com aproximação constante para a versão mais geral onde k hotlinks podem ser atribuídos a cada nó. Na segunda parte deste trabalho, consideramos o problema de computar estratégias eficientes para realizar buscas em árvores. Como uma generalização da tradicional busca binária em listas ordenadas, suponha que se deseja encontrar um nó específico (porém desconhecido) de uma árvore realizando consultas em seus arcos, onde cada consulta indica a extremidade do arco mais próxima ao nó desejado. Dada a probabilidade de cada nó ser aquele procurado, o objetivo é computar uma estratégia de busca que minimize o número esperado de consultas. Aplicações práticas desse problema incluem sincronização de file systems e testes de software. Apresentamos um algoritmo linear que obtém a primeira aproximação constante para esse problema. Isso representa uma melhora significativa em relação à O(log n)-aproximação anterior. / [en] Here we present a study on two optimization problems in trees: the k- Hotlink Assignment Problem and the problem of Binary Searching in Trees. As a result, we obtain improved approximation algorithms for both problem. The k-Hotlink Assignment Problem can be defined as follows. Let G = (V,E) be a directed acyclic graph representing a web site, where nodes correspond to pages and arcs to hyperlinks. In this context, hotlinks are defined as shortcuts (new arcs) added to web pages of G in order to reduce the time spent by users to reach their desired information. Here we consider the problem where G is a rooted directed tree and the goal is minimizing the expected time spent by users by assigning at most k hotlinks to each node. For the most studied version of this problem where at most one hotlink can be assigned from each node, we prove the existence of an FPTAS, improving upon the constant factor algorithm recently obtained in [Jacobs, WADS 2007]. In addition, we develop the first constant factor approximation algorithm for the most general version where k hotlinks can be assigned from each node. In the second part of this work, we consider the problem of computing efficient strategies for searching in trees. As a generalization of the classical binary search for ordered lists, suppose one wishes to find a (unknown) specific node of a tree by asking queries to its arcs, where each query indicates the endpoint closer to the desired node. Given the likelihood of each node being the one searched, the objective is to compute a search strategy that minimizes the expected number of queries. Practical applications of this problem include file system synchronization and software testing. Here we present a linear time algorithm which is the first constant factor approximation for this problem. This represents a significant improvement over previous O(log n)-approximation.

Approximation algorithms are widely used for problems related to computational geometry, complex optimization problems, discrete min-max problems and NP-hard and space hard problems. Due to the complex nature of such problems, imperative languages are perhaps not the best-suited solution when it comes to their actual implementation. Functional languages like Haskell could be a good candidate for the aforementioned mentioned issues. Haskell is used in industries as well as in commercial applications, e.g., concurrent applications, statistics, symbolic math and financial analysis. Several approximation algorithms have been proposed for different problems that naturally arise in the DNA clone classifications. In this thesis, we have performed an initial and explorative study on applying functional languages for approximation algorithms. Specifically, we have implemented a well known approximate clustering algorithm both in Haskell and in Java and we discuss the suitability of applying functional languages for the implementation of approximation algorithms, in particular for graph theoretical approximate clustering problems with applications in DNA clone classification. We also further explore the characteristics of Haskell that makes it suitable for solving certain classes of problems that are hard to implement using imperative languages. / Muhammad Imran Shafi: 29A Sodergatan 19547 Marsta, 0737171514, Muhammad Akram C/O Saad Bin Azhar Folkparksvagen 20/10 Ronneby, 0762899111

As we are currently in the information age, people expect access to information to exist by default. In order to facilitate the communication of knowledge, efficient networks must be built. In particular, the networks must be built satisfying some constraints while minimizing cost or time. These constraints often make these problems NP-hard. In this thesis, we investigate two different sets of problems: communicating information quickly and building cheap networks. In the communication problems, the goal is to minimize the number of rounds of communication. In the network design problems the goal is to construct a network of minimum cost.

Au cours de cette thèse, l'exploration de l'espace de solutions par des métaheuristiques est abordée. Les métaheuristiques sont des méthodes d'optimisation utilisées pour résoudre des problèmes NP-difficile. Elles explorent aléatoirement l'espace de recherche pour trouver les meilleures solutions. Dans un premier temps, l'ensemble des solutions est modélisé par un espace unidimensionnel par une Méthode de Conversion de l'Espace de recherche (MCE). Des métriques sont proposées pour évaluer l'exploration de l'espace de recherche par une métaheuristique en identifiant les zones explorées et inexplorées. Ces métriques sont utilisées pour orienter l'exploration de l'espace de recherche d'une méthode d'optimisation.La convergence est améliorée en accentuant le recherche dans les zones explorées. Pour sortir des minimums locaux, l'exploration est diversifiée en la dirigeant vers les zones inexplorées. En associant l'exploration du voisinage des solutions et ces métriques cartographiques, il est possible d'améliorer les performances des métaheuristiques. Plusieurs algorithmes mono-objectifs et multiobjectifs sont implémentés en version classique, hybridé par la recherche locale et par la MCE. Le Flexible Job Shop Problem (FJSP) est utilisé comme problème de référence. Les expérimentations avec les algorithmes hybridés montrent une amélioration des performances / In this thesis, the solution space exploration by the metaheuristic is developed. The metaheuristics optimization methods are used to solve NP-hard problems. They explore randomly the search space to look for the best solutions. In a first step, the solution set is modeled by a one-dimensional space by a Mapping Method (MaM). Metrics are proposed to evaluate the search space exploration by a metaheuristic, identifying the explored and unexplored zones. These metrics are used to guide the search space exploration of an optimization method. The convergence is improved by emphasizing the research in the zones explored. To get out local minima, the exploration is diversified by pointing it towards the unexplored zones. Combining the neighbour discovery of the solutions and these mapping metrics, it is possible to improve the performance of metaheuristics. Several single-objective and multi-objective algorithms are implemented in the classic version, hybridized with local search and MaM. The Flexible Job Shop Problem (FJSP) is used as a reference problem. The experimentations with hybridized algorithms show performance improved

O problema da árvore geradora de comunicação ótima recebe um grafo com comprimentos não negativos nas arestas e um requerimento não negativo entre cada par de vértices; sendo o objetivo encontrar uma árvore geradora do grafo que minimize o custo de comunicação, que é a soma sobre cada par de vértice da distância entre eles na árvore vezes o requerimento entre eles. Este problema é NP-difícil, assim como vários casos particulares dele. Neste trabalho estudamos algumas variantes deste problema, introduzimos novos casos particulares que são também NP-difíceis e propomos esquemas de aproximação polinomial para alguns deles. / The optimum communication spanning tree problem receives a graph with non-negative lengths over the edges and non-negative requirements for each pair of nodes; being the objective to find a spanning tree of the graph that minimizes the communication cost, which is given by the sum, over each pair of nodes, of the distance, in the tree, between the nodes multiplied by the requirement between them. This problem and several of its particular cases are NP-hard. In this work we study some of the variants, also we introduce new NP-hard particular cases of the problem and propose polynomial approximation schemes for some of them.

Distributed Approximation is a new and rapidly developing discipline that lies at the crossroads of various well-established areas of Computer Science - Distributed Computing, Approximation Algorithms, Graph Theory and often, Computational Geometry. This thesis focuses on the design and analysis of distributed algorithms to solve optimization problems that usually arise in large-scale, heavily dynamic, resource constrained networks, e.g. wireless ad-hoc and sensor networks, P2P systems, mobile networks etc. These problems can often be abstracted by variations of well-known combinatorial optimization problems, such as topology control, clustering etc. Many of these problems are known to be hard (NP-complete). But we need fast and light-weight distributed algorithms for these problems, that yield near-optimal solutions. The results presented in this thesis can be broadly divided in two parts. The first part contains a set of results that obtain improved solutions to the classic problem of computing a sparse "backbone" for Wireless Sensor Networks (WSNs). In graph-theoretic terms, the goal is to compute a spanning subgraph of the input graph, that is sparse, lightweight and has low stretch. The term "low stretch" indicates that in spite of dropping many edges, the distance between any two nodes in the graph is not increased by much. We model WSNs as geometric graphs - unit ball graphs, quasi-unit ball graphs etc. in Euclidean spaces, as well as in more general metric spaces of low doubling dimension. We identify and exploit a variety of geometric features of those models to obtain our results. In the second part of the thesis we focus on distributed algorithms for clustering problems. We present several distributed approximation algorithms for clustering problems (e.g., minimum dominating set, facility location problems) that improve on best known results so far. The main contribution here is the design of distributed algorithms where the running time is a "tunable" parameter. The advent of distributed systems of unprecedented scale and complexity motivates the question of whether it is possible to design algorithms that can provide non-trivial approximation guarantees even after very few rounds of computation and message exchanges. We call these algorithms "k-round algorithms". We design k-round algorithms for various clustering problems that yield non-trivial approximation factors even if k is a constant. Additionally, if k assumes poly-logarithmic values, our algorithms match or improve on the best-known approximation factors for these problems.

abstract: This thesis addresses the following fundamental maximum throughput routing problem: Given an arbitrary edge-capacitated n-node directed network and a set of k commodities, with source-destination pairs (s_i,t_i) and demands d_i> 0, admit and route the largest possible number of commodities -- i.e., the maximum throughput -- to satisfy their demands. The main contributions of this thesis are three-fold: First, a bi-criteria approximation algorithm is presented for this all-or-nothing multicommodity flow (ANF) problem. This algorithm is the first to achieve a constant approximation of the maximum throughput with an edge capacity violation ratio that is at most logarithmic in n, with high probability. The approach used is based on a version of randomized rounding that keeps splittable flows, rather than approximating those via a non-splittable path for each commodity: This allows it to work for arbitrary directed edge-capacitated graphs, unlike most of the prior work on the ANF problem. The algorithm also works if a weighted throughput is considered, where the benefit gained by fully satisfying the demand for commodity i is determined by a given weight w_i>0. Second, a derandomization of the algorithm is presented that maintains the same approximation bounds, using novel pessimistic estimators for Bernstein's inequality. In addition, it is shown how the framework can be adapted to achieve a polylogarithmic fraction of the maximum throughput while maintaining a constant edge capacity violation, if the network capacity is large enough. Lastly, one important aspect of the randomized and derandomized algorithms is their simplicity, which lends to efficient implementations in practice. The implementations of both randomized rounding and derandomized algorithms for the ANF problem are presented and show their efficiency in practice. / Dissertation/Thesis / Masters Thesis Computer Science 2020

The work deals with processing of radio received signal strength in IEEE 802.15.4 which communicates in 2.4 GHz ISM band. The signal is processed by the three approximation methods. They are tested for their effectiveness for measuring in different radio environments. Furthermore, the work deals with calculation of the most efficient coefficients for distance calculating by radio transmission fucntions. It defines the issues of such solutions on practical examples. The work also deals with the experimental algorithm for implementing dynamic calibration of the coefficients. It describes the design, processing and verification of this system in practice.

<div>We consider the maximum vertex-weighted matching problem (MVM), in which non-negative weights are assigned to the vertices of a graph, and the weight of a matching is the sum of the weights of the matched vertices. Vertex-weighted matchings arise in many applications, including internet advertising, facility scheduling, constraint satisfaction, the design of network switches, and computation of sparse bases for the null space or the column space of a matrix. Let m be the number of edges, n number of vertices, and D the maximum degree of a vertex in the graph. We design two exact algorithms for the MVM problem with time complexities of O(mn) and O(Dmn). The new exact algorithms use a maximum cardinality matching as an initial matching, after which the weight of the matching is increased using weight-increasing paths.</div><div><br></div><div>Although MVM problems can be solved exactly in polynomial time, exact MVM algorithms are still slow in practice for large graphs with millions and even billions of edges. Hence we investigate several approximation algorithms for MVM in this thesis. First we show that a maximum vertex-weighted matching can be approximated within an approximation ratio arbitrarily close to one, to k/(k + 1), where k is related to the length of augmenting or weight-increasing paths searched by the algorithm. We identify two main approaches for designing approximation algorithms for MVM. The first approach is direct; vertices are sorted in non-increasing order of weights, and then the algorithm searches for augmenting paths of restricted length that reach a heaviest vertex. (In this approach each vertex is processed once). The second approach repeatedly searches for augmenting paths and increasing paths, again of restricted length, until none can be found. In this second, iterative approach, a vertex may need to be processed multiple times. We design two approximation algorithms based on the direct approach with approximation ratios of 1/2 and 2/3. The time complexities of the 1/2-approximation algorithm is O(m + n log n), and that of the 2/3-approximation algorithm is O(mlogD). Employing the second approach, we design 1/2- and 2/3-approximation algorithms for MVM with time complexities of O(Dm) and O(D²m), respectively. We show that the iterative algorithm can be generalized to nd a k/(k+1)-approximate MVM with a time complexity of O(D^km). In addition, we design parallel 1/2- and 2/3-approximation algorithms for a shared memory programming model, and introduce a new technique for locking augmenting paths to avoid deadlock and related problems. </div><div><br></div><div>MVM problems may be solved using algorithms for the maximum edge-weighted matching (MEM) by assigning to each edge a weight equal to the sum of the vertex weights on its endpoints. However, our results will show that this is one way to generate MEM problems that are difficult to solve. On such problems, exact MEM algorithms may require run times that are a factor of a thousand or more larger than the time of an exact MVM algorithm. Our results show the competitiveness of the new exact algorithms by demonstrating that they outperform MEM exact algorithms. Specifically, our fastest exact algorithm runs faster than the fastest MEM implementation by a factor of 37 and 18 on geometric mean, using two different sets of weights on our test problems. In some instances, the factor can be higher than 500. Moreover, extensive experimental results show that the MVM approximation algorithm outperforms an MEM approximation algorithm with the same approximation ratio, with respect to matching weight and run time. Indeed, our results show that the MVM approximation algorithm outperforms the corresponding MEM algorithm with respect to these metrics in both serial and parallel settings.</div>