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In recent years, sustainable investments have risen in popularity as a result of climate change. However, there is a shortage of reliable tools to aid investors in allocating their funds more sustainably, while still ensuring maximum profitability. Another issue introduced in connection with climate change is greenwashing - companies falsely marketing themselves as sustainable without working on minimizing their environmental impact. The aim of the project is to solve the aforementioned problems and investigate the cost of deterring from profitability for sustainability.  This paper explores if there is a way to allocate a stock portfolio to ensure optimally while taking sustainability into account. The method features predicting the future revenue of stocks, evaluating and quantifying sustainability from companies, and optimizing the portfolio in order to find the optimal set of stocks. The optimization is performed using dynamic programming by treating the problem as a Knapsack Problem. The algorithm is evaluated for two investor profiles - with focus on profitability and with focus on sustainability. The results concluded in a set of shares following a stationary distribution for both investment profiles. Consequently, it is reasoned that Dynamic Programming is a suitable method of optimization within the scope of the thesis however it is also reasoned that improvements can be made to include more sophisticated optimization methods. The cost of selecting the more sustainable option is determined to adhere to a linear relation for all budget levels. / Under de senaste åren har intresset ökat för hållbara investering till följd av klimatkrisen. Den snabba förändringen har emellertid medfört att det inte finns tillförlitliga hjälpverktyg tillgängliga för investerare att fördela sin tillgångar. Ännu ett problem som har dykt upp i samband med klimatkrisen är greenwashing - att företag marknadsför sig som miljövänliga, utan att försöka minska sin klimatpåverkan. Projektets mål är att försöka lösa dem nämnda problemen, samt att undersöka förlusten av att prioritera hållbarhet före lönsamhet.  Syftet med denna uppsats är att utforska möjligheterna med att optimera en aktieportfölj när hållbarhet betraktas som värderingsfaktor. Metoden omfattar att bestämma aktiernas förväntade framtida avkastning, utvärdering och modellering av företags hållbarhetsarbete samt optimering av portföljen. I detta projekt tillämpades dynamisk programmering som optimeringsmetod. Algoritmen utvärderas för två investerings profiler - en som prioriterar lönsamhet och en som prioriterar hållbarhet. Undersökningsresultaten visar att den optimala portföljen följer en stationär fördelning i båda fallen. Följaktligen dras slutsatsen att dynamisk programmering är en tillräckligt bra optimeringsmetod inom undersökningens avgränsningar men att det i framtiden går att införa förbättringar för att ta hänsyn till mer sofistikerade optimeringsmetoder. Det visas även att kostnaden för frångå lönsamhet beskrivs av ett linjärt samband på ala budgetnivåer.

This work addresses two novel problems in the field of computational genomics. The first is whole genome alignment and the second is inferring horizontal gene transfer using posets. We define these two problems and present algorithmic approaches for solving them. For the whole genome alignment, we define alignment graphs for representing different evolutionary events, and define a scoring function for those graphs. The problem defined is proven to be NP-complete. Two heuristics are presented to solve the problem, one is a dynamic programming approach that is optimal for a class of sequences that we define in this work as breakable arrangements. And, the other is a greedy approach that is not necessarily optimal, however, unlike the dynamic programming approach, it allows for reversals. For inferring horizontal gene transfer, we define partial order sets among species, with respect to different genes, and infer genes involved in horizontal gene transfer by comparing posets for different genes. The posets are used to construct a tree for each gene. Those trees are then compared and tested for contradiction, where contradictory trees correspond to genes that are candidates of horizontal gene transfer. / Ph. D.

This dissertation consists of three essays in theoretical and applied microeconomics: the first essay is in cooperative game theory, and the second and third essays relate to forest economics. The first chapter studies a class of cooperative games dubbed ``r-essential games''. Cooperative game theory has proposed different notions of powerful players. For example, big-boss games (Muto et al., 1988) and clan games (Potters et al., 1989) are particular cases of veto games (Bahel, 2016). The first chapter extends these veto games by assuming that there is a given subset of powerful (or essential) players, but only a few (as opposed to all) essential players are required for a coalition to have a positive value. The resulting games, which are called r-essential games, encompass convex games (Shapley, 1971) and veto games. We show that r-essential games have a nonempty core. We give a recursive description of the core. Moreover, it is shown that the core and the bargaining set are equivalent for every r-essential game. An application to networks is provided. The second chapter employs a two-principal, one-agent model to estimate the social cost of fiscal federalism in China's northeast native forests. China's key forested region is located in the northeast and consists of state forest enterprises which manage forest harvesting and reforestation. Deforestation is a major problem there and has resulted in several central government reforms. We develop a framework for assessing the social cost of state forest enterprise deforestation. We first develop a two-principal, one-agent model that fits the federalistic organization of state forests, in that state forest managers make (potentially hidden) decisions under influence of provincial and central government policies. This model is used to quantify the social cost of these hidden actions. We then use panel data from a survey conducted by Peking University to compute social welfare losses and to formally identify the main factors in these costs. A sensitivity analysis shows that, interestingly, command and control through lower harvesting limits and a more accurate monitoring system are more important to lowering social welfare losses than conventional incentives targeting the wages of forest managers. Through regression analysis we also find that the more remote areas with a higher percentage of mature natural forests are the ones that will always have the highest social welfare losses. The third chapter studies the problem of choosing a rotation under uncertain future ecosystem values and timber prices. This problem is nearly as old as the field of forest economics itself. A forest owner faces various uncertainties caused by climate change and market shocks, due to its long-term nature of production and the joint production of interrelated timber and amenity (non-harvesting) benefit streams. The vast literature in stochastic rotation problems simply assumes a known probability distribution for whatever parameter is uncertain, but this type of assumption may lead to misspecification of a rotation decision model if a forest owner has no such information. We study a more relevant question of how to choose rotation ages when there is pure (or Knightian) uncertainty, in that the forest owner does not know distributional features of parameters and further can be averse to this type of information deficit. This chapter is the first to investigate pure uncertainty in amenity benefit streams and is also the first to analytically solve a stochastic rotation problem under pure uncertainty in either amenity streams or market prices. We use robust methods developed in macroeconomics that are particularly suited to forest capital investment problem, but with important differences owing to the nature of forest goods production. The results show that newer models suggesting rotation ages could be longer under volatile parameter distributions do not hold generally when pure uncertainty and forest owner uncertainty aversion is considered. Rather, the earlier literature showing faster or greater harvesting with increases in risk under risk neutrality may actually be a more general result than current literature supposes. In particular, we find that a landowner tends to harvest more when his degree of uncertainty aversion is higher and the model is misspecified by assumption, or when the volatility of an uncertain process is higher. These situations tend to magnify model misspecification costs, especially because the forest manager always assumes the worst case will happen when there is uncertainty. This implies the decision maker is pessimistic in the sense that he or she is always trying to maximize the utility under the worst possible state of nature (the lowest amenity benefit or the lowest timber price). Whether landowners are in fact uncertainty averse and assume the worst case in their decisions remains to be empirically investigated, but our work suggests it is an important question that must be answered. / Doctor of Philosophy / This dissertation consists of three essays in theoretical and applied microeconomics: the first essay is in cooperative game theory, and the second and third essays relate to forest economics. The first chapter studies a class of cooperative games dubbed ``r-essential games''. Cooperative game theory has proposed different notions of powerful players. For example, veto games (Bahel, 2016) have powerful players that are named veto players. Any coalition needs to include all these powerful players to achieve a positive coalition value. The first chapter extends these veto games by assuming that there is a given subset of powerful (or essential) players, but only a few (as opposed to all) essential players are required for a coalition to have a positive value. The resulting games, which are called r-essential games, encompass two classic games, convex games (Shapley, 1971) and veto games. We show that each r-essential game has at least one solution that is an allocation guaranteeing that no coalition can do better on its own. We provide a process allowing to compute this allocation in each r-essential game. An application to networks is provided. The second chapter estimates the damage of deforestation in China's northeast forests. This region consists of state forest enterprises which manage harvesting and reforestation and have represented the most important source of wood supplies since the 1950s. Deforestation is a major problem there. We develop a framework for assessing the damage to the society because of deforestation. We develop a theoretical model to describe the forest management structure, in which state forest managers make (potentially hidden) decisions under influence of provincial and central government policies. This model is used to quantify the damage. We then use data from a survey conducted by Peking University to compute the damage and confirm the main factors in these damages in practice. We find that lower harvesting limits and a more accurate monitoring system are the keys to lowering the damage. These are more important than conventional instruments used by the governments such as the wages for managers that achieve certain targets. We also find that the remote areas with a higher percentage of mature natural forests are the ones that will always have the largest damage. These areas are the hardest to monitor, but our results show they must be a critical focus moving forward. The third chapter studies when should a forest owner harvest under uncertain future ecosystem values and timber prices. A forest owner faces various uncertainties caused by climate change and market shocks, due to its long-term nature of production and the joint production of interrelated timber and non-harvesting benefit streams (such as the recreation value, the biodiversity value and the clean air supported by forests). Previous studies assume a known probability distribution for whatever parameter is uncertain, but this type of assumption may lead to a wrong decision model if a forest owner has no such information. We study a more relevant question of how to choose when to harvest with pure uncertainty, in that the forest owner does not know distributional features of parameters and further can be averse to this type of information deficit. This chapter is the first to investigate pure uncertainty and is also the first to analytically solve a harvest decision making problem under pure uncertainty in either non-harvesting benefit streams or market prices. We use macroeconomics methods that are particularly suited to forest capital investment problem. We find that a landowner tends to harvest more when there is pure uncertainty. Because the forest manager is pessimistic and always thinks the worst case will happen when there is uncertainty.

Water quality management for agricultural production is a complicated and interesting problem. Hydrological and economic factors must be considered when designing strategies to reduce nutrient runoff from agricultural activities. This dissertation is composed of three chapters that investigate cost-effective ways to mitigate water pollution from agricultural nonpoint pollution sources and explore farmers' incentives when participating in water quality trading programs. Chapter 1 investigates landscape targeting of best management practices (BMPs) based on topographic index (TI) to determine how targeting would affect costs of meeting nitrogen (N) loading goals for Mahantango watershed, Pennsylvania. We use the results from two climate models and the mean of the ensemble of seven climate models to estimate expected climate changes and the Soil and Water Assessment Tool-Variable Source Area (SWAT-VSA) model to predict crop yields and N export. Costs of targeting and uniform placement of BMPs across the entire study area (4.23 km2) are compared under historical and future climate scenarios. We find that with a goal of reducing N loadings by 25%, spatial targeting methods could reduce costs by an average of 30% compared with uniform BMP placement under three historical climate scenarios. Cost savings from targeting are 38% under three future climate scenarios. Chapter 2 scales up the study area to the Susquehanna watershed (71,000 km2). We examine the effects of targeting the required reductions in N runoff within counties, across counties, and both within and across counties for the Susquehanna watershed. We set the required N reduction to 35%. Using the uniform strategy to meet the required N reduction as the baseline, results show that costs of achieving a regional 35% N reduction goal can be reduced by 13%, 31% and 36% with cross-county targeting, within-county targeting and within and across county targeting, respectively. Results from Chapters 1 and 2 suggest that cost effectiveness of government subsidy programs for water quality improvement in agriculture can be increased by targeting them to areas with lower N abatement costs. In addition, targeting benefits are likely to be even larger under climate change. Chapter 3 investigates the landowner's nutrient credit trading behavior when facing the price uncertainty given the credits are allowed to be banked for future use. A two-step decision model is used in this study. For the first step, we determine the landowner's application level of a BMP on working land in the initial time period. The nutrient credits awarded to the landowner depend on the nutrient reduction level at the edge of field generated by the BMP application. For the second step, we use an intertemporal model to examine the landowner's credit trading behavior with stochastic price fluctuations over time and with transaction costs. The theoretical framework is applied with a numerical simulation incorporated with a hydro-economic model and dynamic programming. Nutrient Management (NM) is selected as the BMP on working land to generate N credits. We find that gains to the landowner from credit banking increase with higher price volatility and with higher price drift, but that gains are larger with price volatility. However, for a landowner holding a small amount of nutrient credits, the gains from credit banking are small due to transaction costs. / Doctor of Philosophy / Two considerations are critical for efforts to mitigate nutrient runoff from nonpoint sources: cost effectiveness of strategies to reduce nutrient runoff and landowners' incentives to participate in these programs. This dissertation is composed of three manuscripts, aiming to evaluate the cost effectiveness of government subsidy programs for water quality management in agriculture and investigate the landowner's incentives to participate in water quality trading programs for the Chesapeake Bay watershed. Chapter 1 investigates gains from targeting Best Management Practices (BMPs) under current and future climate conditions based on the soil characteristics relative to uniform BMP application for a small experimental watershed (4.23km2). Chapter 2 scales up the study area to a 71,000 km2 watershed and treats each county within the watershed as a representative farm to explore economic gains from targeting within county and across county based on counties' physical conditions and agricultural patterns. Both Chapters show that cost-effectiveness of government subsidy programs can be improved by spatial targeting BMPs to areas with lower abatement costs. Gains from targeting increase under climate change. In Chapter 3 we shows how a landowner's revenues from nutrient credit selling will be affected if the credits are allowed to be banked for future use when she faces price uncertainty. We find that gains to the landowner from credit banking increase more with higher price volatility than with higher price drift. Gains from banking are largely reduced by transaction costs associated with trading.

Optimal Control (OC) is essentially a mathematical extremal problem. The procedure consists on the definition of a criterion to minimize (or maximize), some constraints that must be fulfilled and boundary conditions or disturbances affecting to the system behavior. The OC theory supplies methods to derive a control trajectory that minimizes (or maximizes) that criterion. This dissertation addresses the application of OC to automotive control problems at the powertrain level, with emphasis on the internal combustion engine. The necessary tools are an optimization method and a mathematical representation of the powertrain. Thus, the OC theory is reviewed with a quantitative analysis of the advantages and drawbacks of the three optimization methods available in literature: dynamic programming, Pontryagin minimum principle and direct methods. Implementation algorithms for these three methods are developed and described in detail. In addition to that, an experimentally validated dynamic powertrain model is developed, comprising longitudinal vehicle dynamics, electrical motor and battery models, and a mean value engine model. OC can be utilized for three different purposes: 1. Applied control, when all boundaries can be accurately defined. The engine control is addressed with this approach assuming that a the driving cycle is known in advance, translating into a large mathematical problem. Two specific cases are studied: the management of a dual-loop EGR system, and the full control of engine actuators, namely fueling rate, SOI, EGR and VGT settings. 2. Derivation of near-optimal control rules, to be used if some disturbances are unknown. In this context, cycle-specific engine calibrations calculation, and a stochastic feedback control for power-split management in hybrid vehicles are analyzed. 3. Use of OC trajectories as a benchmark or base line to improve the system design and efficiency with an objective criterion. OC is used to optimize the heat release law of a diesel engine and to size a hybrid powertrain with a further cost analysis. OC strategies have been applied experimentally in the works related to the internal combustion engine, showing significant improvements but non-negligible difficulties, which are analyzed and discussed. The methods developed in this dissertation are general and can be extended to other criteria if appropriate models are available. / El Control Óptimo (CO) es esencialmente un problema matemático de búsqueda de extremos, consistente en la definición de un criterio a minimizar (o maximizar), restricciones que deben satisfacerse y condiciones de contorno que afectan al sistema. La teoría de CO ofrece métodos para derivar una trayectoria de control que minimiza (o maximiza) ese criterio. Esta Tesis trata la aplicación del CO en automoción, y especialmente en el motor de combustión interna. Las herramientas necesarias son un método de optimización y una representación matemática de la planta motriz. Para ello, se realiza un análisis cuantitativo de las ventajas e inconvenientes de los tres métodos de optimización existentes en la literatura: programación dinámica, principio mínimo de Pontryagin y métodos directos. Se desarrollan y describen los algoritmos para implementar estos métodos así como un modelo de planta motriz, validado experimentalmente, que incluye la dinámica longitudinal del vehículo, modelos para el motor eléctrico y las baterías, y un modelo de motor de combustión de valores medios. El CO puede utilizarse para tres objetivos distintos: 1. Control aplicado, en caso de que las condiciones de contorno estén definidas. Puede aplicarse al control del motor de combustión para un ciclo de conducción dado, traduciéndose en un problema matemático de grandes dimensiones. Se estudian dos casos particulares: la gestión de un sistema de EGR de doble lazo, y el control completo del motor, en particular de las consignas de inyección, SOI, EGR y VGT. 2. Obtención de reglas de control cuasi-óptimas, aplicables en casos en los que no todas las perturbaciones se conocen. A este respecto, se analizan el cálculo de calibraciones de motor específicas para un ciclo, y la gestión energética de un vehículo híbrido mediante un control estocástico en bucle cerrado. 3. Empleo de trayectorias de CO como comparativa o referencia para tareas de diseño y mejora, ofreciendo un criterio objetivo. La ley de combustión así como el dimensionado de una planta motriz híbrida se optimizan mediante el uso de CO. Las estrategias de CO han sido aplicadas experimentalmente en los trabajos referentes al motor de combustión, poniendo de manifiesto sus ventajas sustanciales, pero también analizando dificultades y líneas de actuación para superarlas. Los métodos desarrollados en esta Tesis Doctoral son generales y aplicables a otros criterios si se dispone de los modelos adecuados. / El Control Òptim (CO) és essencialment un problema matemàtic de cerca d'extrems, que consisteix en la definició d'un criteri a minimitzar (o maximitzar), restriccions que es deuen satisfer i condicions de contorn que afecten el sistema. La teoria de CO ofereix mètodes per a derivar una trajectòria de control que minimitza (o maximitza) aquest criteri. Aquesta Tesi tracta l'aplicació del CO en automoció i especialment al motor de combustió interna. Les ferramentes necessàries són un mètode d'optimització i una representació matemàtica de la planta motriu. Per a això, es realitza una anàlisi quantitatiu dels avantatges i inconvenients dels tres mètodes d'optimització existents a la literatura: programació dinàmica, principi mínim de Pontryagin i mètodes directes. Es desenvolupen i descriuen els algoritmes per a implementar aquests mètodes així com un model de planta motriu, validat experimentalment, que inclou la dinàmica longitudinal del vehicle, models per al motor elèctric i les bateries, i un model de motor de combustió de valors mitjans. El CO es pot utilitzar per a tres objectius diferents: 1. Control aplicat, en cas que les condicions de contorn estiguen definides. Es pot aplicar al control del motor de combustió per a un cicle de conducció particular, traduint-se en un problema matemàtic de grans dimensions. S'estudien dos casos particulars: la gestió d'un sistema d'EGR de doble llaç, i el control complet del motor, particularment de les consignes d'injecció, SOI, EGR i VGT. 2. Obtenció de regles de control quasi-òptimes, aplicables als casos on no totes les pertorbacions són conegudes. A aquest respecte, s'analitzen el càlcul de calibratges específics de motor per a un cicle, i la gestió energètica d'un vehicle híbrid mitjançant un control estocàstic en bucle tancat. 3. Utilització de trajectòries de CO com comparativa o referència per a tasques de disseny i millora, oferint un criteri objectiu. La llei de combustió així com el dimensionament d'una planta motriu híbrida s'optimitzen mitjançant l'ús de CO. Les estratègies de CO han sigut aplicades experimentalment als treballs referents al motor de combustió, manifestant els seus substancials avantatges, però també analitzant dificultats i línies d'actuació per superar-les. Els mètodes desenvolupats a aquesta Tesi Doctoral són generals i aplicables a uns altres criteris si es disposen dels models adequats. / Reig Bernad, A. (2017). Optimal Control for Automotive Powertrain Applications [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90624

This research presents a two-part study on a fuel cell electric van (FCEV), focusing on vehicle modelling and developing different control strategies for the modelled vehicle. The modelling phase accounts for the aging effects on the fuel cell (FC) and battery, analyzing FCEV behavior over time. This includes estimating and integrating the degradation impacts on characteristic curves, such as the FC’s polarization and efficiency curves, the battery’s charging and discharging resistance curves, and the open-circuit voltage curve. A simplified fuel cell system (FCS) model is designed to consider power losses in multiple components, including the FC stack, air compressor, and others. The dynamic limits of the FC are also included to yield more realistic results. The model is based on the vehicle Opel Vivaro FC specifications, incorporating parameters like maximum FC power, battery capacity, vehicle weight, and tire dimensions. Subsequently, various control strategies are applied to analyze their effectiveness in FC and battery State-of-Health (SOH) degradation and hydrogen consumption. A rule-based energy management system (EMS) is implemented first, which operates with five different operational modes dependent on the vehicle’s state. This is followed by a look-up table (LUT) based strategy, which uses two two-dimensional tables generated by a Neural Network (NN). The network is trained with discretized optimal / Thesis / Master of Applied Science (MASc)

Transforming the aging electric grid to a smart grid is an active area of research in industry and the government. One of the main objectives of the smart grid is to improve the efficiency of power generation, transmission and distribution and also to improve the stability and the reliability of the grid. In order to achieve this, various processes involved in power generation, transmission, and distribution should be armed with advanced sensor technologies, computing, communication and networking capabilities to an unprecedented level. These high speed data transfer and computational abilities aid power system engineers to obtain wide area measurements, achieve better control of power system operations and improve the reliability of power supply and the efficiency of different power grid operations. In the process of making the grid smarter, problems existing in traditional grid applications can be identified and solutions have to be developed to fix the identified issues. In this dissertation, two problems that aid power system engineers to meet the above mentioned smart grid's objective are researched. One problem is related to the distribution-side smart grid and the other one is a part of the transmission-side smart grid. Advanced Metering Infrastructure (AMI) is one of the important distribution-side smart grid applications. AMI is a technology where smart meters are installed at customer site which gives the utilities the ability to monitor and collect information related to the amount of electricity, water, and gas consumed by the user. Many recent research studies suggested the use of 3G cellular CDMA2000 for AMI network as it provides an advanced and cost effective solution for smart grid communications. Taking into account both technical and non-technical factors such as extended lifetime, security, availability and control of the solution, Alliander, an electric utility in Netherlands deployed a private 3G CDMA2000 network for smart metering. Although 3G CDMA2000 satisfies the requirements of smart grid applications, an analysis on the use of the current state of the art 3G CDMA2000 for smart grid applications indicates that its usage results in high percentage of control overhead, high latency and high power consumption for data transfer. As a part of this dissertation, we proposed FLEX-MAC - a new Medium Access Control (MAC) protocol that reduces the latency and overhead in smart meter data collection when compared to 3G CDMA2000 MAC. As mentioned above the second problem studied in this dissertation is related to the transmission-side grid. Power grid transmission and sub-transmission lines are generally protected by distance relays. After a thorough analysis of U.S. historical blackouts, North American Electric Reliability Council (NERC) has concluded that the hidden failure induced tripping of distance relays is responsible for 70% of the U.S. blackouts. As a part of this dissertation, agent based distance relaying protection scheme is proposed to improve the robustness of distance relays to hidden failures and thus reduce the probability of blackouts. This dissertation has two major contributions. First, a hierarchically distributed non-intrusive Agent Aided Distance Relaying Protection Scheme (AADRPS) is proposed to improve the robustness of distance relays to hidden failures. The problem of adapting the proposed AADRPS to a larger power system network consisting of thousands of buses is modeled as an integer linear programming multiple facility location optimization problem. Distance relaying protection scheme is a real time system and has stringent timing requirements. Therefore, in order to verify if the proposed AADRPS meets the timing requirements or not and also to check for deadlocks, verification models based on UPPAAL real time model checker are provided in this dissertation. So, the entire framework consisting of AADRPS that aids in increasing the robustness of distance relays and reducing the possibility of blackouts, the multiple facility location optimization models and the UPPAAL real time model checker verification models form one of the major contributions of this dissertation. The second contribution is related to the MAC layer of AMI networks. In this dissertation, FLEX-MAC - a novel and flexible MAC protocol is proposed to reduce the overhead and latency in smart meter data collection. The novelty of the FLEX-MAC lies in its ability to change the mode of operation based on the type of the data being collected in a smart meter network. FLEX-MAC employs Frame and Channel Reserved (FCR) MAC or Frame Reserved and Random Channel (FRRC) MAC for scheduled data collection. Power outage data in an AMI network is considered as a random data . In a densely populated area, during an outage, a large number of smart meters attempt to report the outage, which significantly increases the Random Access CHannel (RACH) load. In order to reduce the RACH traffic during an outage, this dissertation proposes a Time Hierarchical Scheme (THS). Also, in order to minimize the total time to collect the power outage data, a Backward Recursive Dynamic Programming (BRDP) approach is proposed to adapt the transmission rate of smart meters reporting an outage. Both the Optimal Transmission Rate Adaption and Time Hierarchical Scheme form the basis of OTRA-THS MAC which is employed by FLEX-MAC for random data collection. Additionally, in this work, Markov chain models are presented for evaluating the performance of FCR and FRRC MACs in terms of average throughput and delay. Also, another Markov model is presented to find the mean time to absorption or mean time to collect power outage data of OTRA-TH MAC during an outage. / Ph. D.

Die Kernaufgabe der parameterisierten Komplexität ist zu verstehen, wie Eingabestruktur die Problemkomplexität beeinflusst. Wir untersuchen diese Fragestellung aus einer granularen Perspektive und betrachten Problem-Parameter-Kombinationen mit einfach exponentieller Laufzeit, d.h., Laufzeit a^k n^c, wobei n die Eingabegröße ist, k der Parameterwert, und a und c zwei positive Konstanten sind. Unser Ziel ist es, die optimale Laufzeitbasis a für eine gegebene Kombination zu bestimmen. Für viele Zusammenhangsprobleme, wie Connected Vertex Cover oder Connected Dominating Set, ist die optimale Basis bezüglich dem Parameter Baumweite bekannt. Die Baumweite gehört zu der Klasse der Weiteparameter, welche auf natürliche Weise zu Algorithmen mit dem Prinzip der dynamischen Programmierung führen. Im ersten Teil dieser Dissertation untersuchen wir, wie sich die optimale Laufzeitbasis für diverse Zusammenhangsprobleme verändert, wenn wir zu ausdrucksstärkeren Weiteparametern wechseln. Wir entwerfen neue parameterisierte Algorithmen und (bedingte) untere Schranken, um diese optimalen Basen zu bestimmen. Insbesondere zeigen wir für die Parametersequenz Baumweite, modulare Baumweite, und Cliquenweite, dass die optimale Basis von Connected Vertex Cover bei 3 startet, sich erst auf 5 erhöht und dann auf 6, wobei hingegen die optimale Basis von Connected Dominating Set bei 4 startet, erst bei 4 bleibt und sich dann auf 5 erhöht. Im zweiten Teil gehen wir über Weiteparameter hinaus und analysieren restriktivere Arten von Parametern. Für die Baumtiefe entwerfen wir platzsparende Verzweigungsalgorithmen. Die Beweistechniken für untere Schranken bezüglich Weiteparametern übertragen sich nicht zu den restriktiveren Parametern, weshalb nur wenige optimale Laufzeitbasen bekannt sind. Um dies zu beheben untersuchen wir Knotenlöschungsprobleme. Insbesondere zeigen wir, dass die optimale Basis von Odd Cycle Transversal parameterisiert mit einem Modulator zu Baumweite 2 den Wert 3 hat. / The question at the heart of parameterized complexity is how input structure governs the complexity of a problem. We investigate this question from a fine-grained perspective and study problem-parameter-combinations with single-exponential running time, i.e., time a^k n^c, where n is the input size, k the parameter value, and a and c are positive constants. Our goal is to determine the optimal base a for a given combination. For many connectivity problems such as Connected Vertex Cover or Connecting Dominating Set, the optimal base is known relative to treewidth. Treewidth belongs to the class of width parameters, which naturally admit dynamic programming algorithms. In the first part of this thesis, we study how the optimal base changes for these connectivity problems when going to more expressive width parameters. We provide new parameterized dynamic programming algorithms and (conditional) lower bounds to determine the optimal base, in particular, we obtain for the parameter sequence treewidth, modular-treewidth, clique-width that the optimal base for Connected Vertex Cover starts at 3, increases to 5, and then to 6, whereas the optimal base for Connected Dominating Set starts at 4, stays at 4, and then increases to 5. In the second part, we go beyond width parameters and study more restrictive parameterizations like depth parameters and modulators. For treedepth, we design space-efficient branching algorithms. The lower bound techniques for width parameterizations do not carry over to these more restrictive parameterizations and as a result, only a few optimal bases are known. To remedy this, we study standard vertex-deletion problems. In particular, we show that the optimal base of Odd Cycle Transversal parameterized by a modulator to treewidth 2 is 3. Additionally, we show that similar lower bounds can be obtained in the realm of dense graphs by considering modulators consisting of so-called twinclasses.