NP-hard problems have numerous applications in various fields such as networks, computer systems, circuit design, etc. However, no efficient algorithms have been found for NP-hard problems. It has been commonly believed that no efficient algorithms for NP-hard problems exist, i.e., that P6=NP. Recently, it has been observed that there are parameters much smaller than input sizes in many instances of NP-hard problems in the real world. In the last twenty years, researchers have been interested in developing efficient algorithms, i.e., fixed-parameter tractable algorithms, for those instances with small parameters. Fixed-parameter tractable algorithms can practically find exact solutions to problem instances with small parameters, though those problems are considered intractable in traditional computational theory. In this dissertation, we propose a new approach of algorithm design and analysis: discovering better measures for problems. In particular we use two measures instead of the traditional single measure?input size to design algorithms and analyze their time complexity. For several classical NP-hard problems, we present improved algorithms designed and analyzed with this new approach, First we show that the new approach is extremely powerful for designing fixedparameter tractable algorithms by presenting improved fixed-parameter tractable algorithms for the 3D-matching and 3D-packing problems, the multiway cut problem, the feedback vertex set problems on both directed and undirected graph and the max-leaf problems on both directed and undirected graphs. Most of our algorithms are practical for problem instances with small parameters. Moreover, we show that this new approach is also good for designing exact algorithms (with no parameters) for NP-hard problems by presenting an improved exact algorithm for the well-known satisfiability problem. Our results demonstrate the power of this new approach to algorithm design and analysis for NP-hard problems. In the end, we discuss possible future directions on this new approach and other approaches to algorithm design and analysis.

Many problems of practical significance are known to be NP-hard, and hence, are unlikely to be solved by polynomial-time algorithms. There are several ways to cope with the NP-hardness of a certain problem. The most popular approaches include heuristic algorithms, approximation algorithms, and randomized algorithms. Recently, parameterized computation and complexity have been receiving a lot of attention. By taking advantage of small or moderate parameter values, parameterized algorithms provide new venues for practically solving problems that are theoretically intractable. In this dissertation, we design efficient parameterized algorithms for several wellknown NP-hard problems and prove strong lower bounds for some others. In doing so, we place emphasis on the development of new techniques that take advantage of the structural properties of the problems. We present a simple parameterized algorithm for Vertex Cover that uses polynomial space and runs in time O(1.2738k + kn). It improves both the previous O(1.286k + kn)-time polynomial-space algorithm by Chen, Kanj, and Jia, and the very recent O(1.2745kk4 + kn)-time exponential-space algorithm, by Chandran and Grandoni. This algorithm stands out for both its performance and its simplicity. Essential to the design of this algorithm are several new techniques that use structural information of the underlying graph to bound the search space. For Vertex Cover on graphs with degree bounded by three, we present a still better algorithm that runs in time O(1.194k + kn), based on an “almost-global” analysis of the search tree. We also show that an important structural property of the underlying graphs – the graph genus – largely dictates the computational complexity of some important graph problems including Vertex Cover, Independent Set and Dominating Set. We present a set of new techniques that allows us to prove almost tight computational lower bounds for some NP-hard problems, such as Clique, Dominating Set, Hitting Set, Set Cover, and Independent Set. The techniques are further extended to derive computational lower bounds on polynomial time approximation schemes for certain NP-hard problems. Our results illustrate a new approach to proving strong computational lower bounds for some NP-hard problems under reasonable conditions.

Much research has been done on wireless sensor networks. However, most protocols and algorithms for such networks are based on the ideal model Unit Disk Graph (UDG) model or do not assume any model. Furthermore, many results assume the knowledge of location information of the network. In practice, sensor networks often deviate from the UDG model significantly. It is not uncommon to observe stable long links that are more than five times longer than unstable short links in real wireless networks. A more general network model, the quasi unit-disk graph (quasi-UDG) model, captures much better the characteristics of wireless networks. However, the understanding of the properties of general quasi-UDGs has been very limited, which is impeding the design of key network protocols and algorithms. In this dissertation we study the properties for general wireless sensor networks and develop new topological/geometrical techniques for wireless sensor networking. We assume neither the ideal UDG model nor the location information of the nodes. Instead we work on the more general quasi-UDG model and focus on figuring out the relationship between the geometrical properties and the topological properties of wireless sensor networks. Based on such relationships we develop algorithms that can compute useful substructures (planar subnetworks, boundaries, etc.). We also present direct applications of the properties and substructures we constructed including routing, data storage, topology discovery, etc. We prove that wireless networks based on quasi-UDG model exhibit nice properties like separabilities, existences of constant stretch backbones, etc. We develop efficient algorithms that can obtain relatively dense planar subnetworks for wireless sensor networks. We also present efficient routing protocols and balanced data storage scheme that supports ranged queries. We present algorithmic results that can also be applied to other fields (e.g., information management). Based on divide and conquer and improved color coding technique, we develop algorithms for path, matching and packing problem that significantly improve previous best algorithms. We prove that it is unlikely for certain problems in operation science and information management to have any relatively effective algorithm or approximation algorithm for them.

A family of parameterized Thue equations is defined as F_{t,s,...}(X, Y ) = m, m ∈ Z where F_{t,s,...}(X,Y) is a form in X and Y with degree greater than or equal to 3 and integer coefficients that are parameterized by t, s, . . . ∈ Z. A variety of these families have been studied by different authors. In this thesis, we study the following families of Thue inequalities |sx3 −tx2y−(t+3s)xy2 −sy3|≤2t+3s, |sx4 −tx3y−6sx2y2 +txy3 +sy4|≤6t+7s, |sx6 − 2tx5y − (5t + 15s)x4y2 − 20sx3y3 + 5tx2y4 +(2t + 6s)xy5 + sy6| ≤ 120t + 323s, where s and t are integers. The forms in question are “simple”, in the sense that the roots of the underlying polynomials can be permuted transitively by automorphisms. With this nice property and the hypergeometric functions, we construct sequences of good approximations to the roots of the underlying polynomials. We can then prove that under certain conditions on s and t there are upper bounds for the number of integer solutions to the above Thue inequalities.

A grande popularidade dos dispositivos móveis que provêm acesso ubíquo à Internet de banda larga, através de redes de rádio, e o volume de tráfego gerado por estes dispositivos estão aumentando a cada ano. Além disso, vem ampliando consideravelmente a frequência com que usuários de dispositivos móveis estão usando serviços baseados na Web. Alguns destes usuários podem estar acessando serviços que precisam de transmissão contínua como, por exemplo, vídeos interativos, outros podem estar apenas lendo e-mails, o que não exige um fluxo contínuo de dados. Mais do que isso, usuários com altos níveis de sinal podem atingir melhores taxas de transferência do que os com níveis menores. Portanto, encontrar a melhor relação entre os usuários que estão acessando serviços sensíveis ao atraso e aqueles que maximizam a taxa de transferência, e ainda ser justo na transmissão, é um relevante desafio para o escalonamento dos recursos de uma rede sem fio. Embora as pesquisas de escalonamento de recursos em redes sem fio tenham evoluído neste sentido, o recente aumento do volume de tráfego mencionado pode levar a uma sobrecarga no sistema, comprometendo o escalonamento. A fim de enfrentar estes desafios, o Orthogonal Frequency Division Multiple Access (OFDMA), tecnologia fundamental para o acesso múltiplo em redes de quarta geração, tem sido considerado também para ser utilizado na próxima geração de rádios móveis. Para implementar um serviço efetivo aos usuários, requisitos, tais como, altas taxas de transferência, tolerância baixa ao atraso, minimização da perda de pacotes e maximização da justiça no escalonamento, devem somar-se à característica, de alta densidade de usuários, que surgiu após o advento da popularização dos dispositivos móveis. Portanto, novas estratégias de escalonamento devem ser idealizadas. Nesta dissertação, deu-se um passo além na proposição de um escalonador para as redes móveis de próxima geração, que busca melhorar a relação entre taxa de transferência e atraso, consequentemente, levando a maiores índices de justiça no escalonamento resultante. O escalonador foi especialmente desenvolvido para lidar com altas densidades de usuários, inerentes às redes modernas, e as redes LTE foram utilizadas como caso de estudo. Desta forma, um novo escalonador ótimo que considera provisão dos requisitos acima mencionados, é modelado. Além disso, uma nova heurística parametrizável, baseada na qualidade do canal do usuário, no atraso permitido por cada serviço e na justiça do escalonamento é proposta, a fim de lidar com cenários sobrecarregados. Resultados demonstram que a abordagem de escalonamento proposta leva a uma taxa de transferência apenas 7,5% menor que os valores ótimos, com 25% a menos de perda de pacotes em cenários sobrecarregados. O modelo também garante que o escalonamento resultante seja pelo menos 0,91 na escala do índice de justiça de Jain. Finalmente, os resultados mostram uma melhor relação entre a eficiência espectral e as métricas de QoS. / The huge popularity of mobile devices that provides a ubiquitous Internet broadband access via radio networks and the volume of traffic generated by these devices in the base stations are increasing every year. Furthermore, the frequency which, mobile users are using web-based services, is increasing, requiring high transfer rates such as transmission of interactive videos. These factors have become the main challenges for the scheduling of radio resources. In order to meet these challenges, the Orthogonal Frequency Division Multiple Access (OFDMA), a key technology for multiple access in fourth generation networks, has also been considered for use in next-generation mobile radios. To implement an effective service to users, requirements such as high transfer rates, lower delay tolerance, minimum packet loss and maximum scheduling fairness, should be added to the requirements that emerged after the advent of the popularity of mobile devices. Therefore, new scheduling strategies should be projected. Despite efforts to solve the downlink (DL) scheduling problem on wireless networks, we are not aware of previous attempts that have addressed the above requirements in a single strategy. In this thesis, we took a step further in this direction and still considering the high densities in small cells inherent in modern networks. In additional, we address the radio DL resource scheduling problem for multiple users using LTE networks as a case study. A new optimal scheduler is modeled regarding Quality of Service (QoS) provisioning. In addition, a parameterized heuristic based on user channel quality and service delay is proposed to reach scheduling solutions for overbooked scenarios. Results demonstrate that the proposed scheduling approaches led to a throughput of 7.5% lower than the optimal ones and 25% lower packet losses in overloaded scenarios. Our model also ensures that the resultant scheduling is at least as fair as 0.91 in Jain fairness index. Additionally, the obtained results show a reasonable trade-off between spectral efficiency and QoS metrics.

A grande popularidade dos dispositivos móveis que provêm acesso ubíquo à Internet de banda larga, através de redes de rádio, e o volume de tráfego gerado por estes dispositivos estão aumentando a cada ano. Além disso, vem ampliando consideravelmente a frequência com que usuários de dispositivos móveis estão usando serviços baseados na Web. Alguns destes usuários podem estar acessando serviços que precisam de transmissão contínua como, por exemplo, vídeos interativos, outros podem estar apenas lendo e-mails, o que não exige um fluxo contínuo de dados. Mais do que isso, usuários com altos níveis de sinal podem atingir melhores taxas de transferência do que os com níveis menores. Portanto, encontrar a melhor relação entre os usuários que estão acessando serviços sensíveis ao atraso e aqueles que maximizam a taxa de transferência, e ainda ser justo na transmissão, é um relevante desafio para o escalonamento dos recursos de uma rede sem fio. Embora as pesquisas de escalonamento de recursos em redes sem fio tenham evoluído neste sentido, o recente aumento do volume de tráfego mencionado pode levar a uma sobrecarga no sistema, comprometendo o escalonamento. A fim de enfrentar estes desafios, o Orthogonal Frequency Division Multiple Access (OFDMA), tecnologia fundamental para o acesso múltiplo em redes de quarta geração, tem sido considerado também para ser utilizado na próxima geração de rádios móveis. Para implementar um serviço efetivo aos usuários, requisitos, tais como, altas taxas de transferência, tolerância baixa ao atraso, minimização da perda de pacotes e maximização da justiça no escalonamento, devem somar-se à característica, de alta densidade de usuários, que surgiu após o advento da popularização dos dispositivos móveis. Portanto, novas estratégias de escalonamento devem ser idealizadas. Nesta dissertação, deu-se um passo além na proposição de um escalonador para as redes móveis de próxima geração, que busca melhorar a relação entre taxa de transferência e atraso, consequentemente, levando a maiores índices de justiça no escalonamento resultante. O escalonador foi especialmente desenvolvido para lidar com altas densidades de usuários, inerentes às redes modernas, e as redes LTE foram utilizadas como caso de estudo. Desta forma, um novo escalonador ótimo que considera provisão dos requisitos acima mencionados, é modelado. Além disso, uma nova heurística parametrizável, baseada na qualidade do canal do usuário, no atraso permitido por cada serviço e na justiça do escalonamento é proposta, a fim de lidar com cenários sobrecarregados. Resultados demonstram que a abordagem de escalonamento proposta leva a uma taxa de transferência apenas 7,5% menor que os valores ótimos, com 25% a menos de perda de pacotes em cenários sobrecarregados. O modelo também garante que o escalonamento resultante seja pelo menos 0,91 na escala do índice de justiça de Jain. Finalmente, os resultados mostram uma melhor relação entre a eficiência espectral e as métricas de QoS. / The huge popularity of mobile devices that provides a ubiquitous Internet broadband access via radio networks and the volume of traffic generated by these devices in the base stations are increasing every year. Furthermore, the frequency which, mobile users are using web-based services, is increasing, requiring high transfer rates such as transmission of interactive videos. These factors have become the main challenges for the scheduling of radio resources. In order to meet these challenges, the Orthogonal Frequency Division Multiple Access (OFDMA), a key technology for multiple access in fourth generation networks, has also been considered for use in next-generation mobile radios. To implement an effective service to users, requirements such as high transfer rates, lower delay tolerance, minimum packet loss and maximum scheduling fairness, should be added to the requirements that emerged after the advent of the popularity of mobile devices. Therefore, new scheduling strategies should be projected. Despite efforts to solve the downlink (DL) scheduling problem on wireless networks, we are not aware of previous attempts that have addressed the above requirements in a single strategy. In this thesis, we took a step further in this direction and still considering the high densities in small cells inherent in modern networks. In additional, we address the radio DL resource scheduling problem for multiple users using LTE networks as a case study. A new optimal scheduler is modeled regarding Quality of Service (QoS) provisioning. In addition, a parameterized heuristic based on user channel quality and service delay is proposed to reach scheduling solutions for overbooked scenarios. Results demonstrate that the proposed scheduling approaches led to a throughput of 7.5% lower than the optimal ones and 25% lower packet losses in overloaded scenarios. Our model also ensures that the resultant scheduling is at least as fair as 0.91 in Jain fairness index. Additionally, the obtained results show a reasonable trade-off between spectral efficiency and QoS metrics.

The Constraint Satisfaction Problem (CSP) is a fundamental NP-complete problem with many applications in artificial intelligence. This problem has enjoyed considerable scientific attention in the past decades due to its practical usefulness and the deep theoretical questions it relates to. However, there is a wide gap between practitioners, who develop solving techniques that are efficient for industrial instances but exponential in the worst case, and theorists who design sophisticated polynomial-time algorithms for restrictions of CSP defined by certain algebraic properties. In this thesis we attempt to bridge this gap by providing polynomial-time algorithms to test for membership in a selection of major tractable classes. Even if the instance does not belong to one of these classes, we investigate the possibility of decomposing efficiently a CSP instance into tractable subproblems through the lens of parameterized complexity. Finally, we propose a general framework to adapt the concept of kernelization, central to parameterized complexity but hitherto rarely used in practice, to the context of constraint reasoning. Preliminary experiments on this last contribution show promising results.

Stalk lodging, or failure of the stalk structure, presents a serious problem in the production of maize (Zea mays L.). Lodged stalks negatively impact crop yields by inhibiting further grain growth and often prevent the harvest of the grain. Addressing this problem requires the development of new maize hybrids that exhibit enhanced lodging resistance, which in turn requires an understanding of the parameters that influence lodging resistance. Current methods make use of specimen-specific geometry and material properties, but these methods have limited ability to examine geometric effects and can require excessive time. A parameterized model of the maize stalk has the potential to overcome these limitations. The purpose of this study was to develop a model of the maize stalk cross-section that could accurately predict transverse stiffness. Principal component analysis was utilized to discover underlying geometric patterns that could be used as parameters in a cross-sectional model. Using the resulting principal components, a series of approximated cross-sections was created that represented various levels of fidelity to real cross-section geometry. The real and approximated cross-sections were modeled in transverse compression with a prescribed deformation load, and the predictive accuracy of each approximated model was calculated. A sensitivity study was also performed to quantify the strength of individual parameter effects. The simplest model, an elliptical cross-section, accurately predicted transverse stiffness while minimizing the number of model parameters. This model may later be used as a basis for a three-dimensional parameterized model of the maize stem.

No description available.

In this paper we describe an approach to generating low-order models of spiral inductors that accurately capture the dependence on both frequency and geometry (width and spacing) parameters. The approach is based on adapting a multiparameter Krylov-subspace based moment matching method to reducing an integral equation for the three dimensional electromagnetic behavior of the spiral inductor. The approach is demonstrated on a typical on-chip rectangular inductor. / Singapore-MIT Alliance (SMA)