Over the past decades, cost-effectiveness principle or cost-benefit analysis has been employed oftentimes as a typical assessment tool for the expansion of drinking water utility. With changing public awareness of the inherent linkages between climate change, population growth and economic development, the addition of global change impact in the assessment regime has altered the landscape of traditional evaluation matrix. Nowadays, urban drinking water infrastructure requires careful long-term expansion planning to reduce the risk from global change impact with respect to greenhouse gas (GHG) emissions, economic boom and recession, as well as water demand variation associated with population growth and migration. Meanwhile, accurate prediction of municipal water demand is critically important to water utility in a fast growing urban region for the purpose of drinking water system planning, design and water utility asset management. A system analysis under global change impact due to the population dynamics, water resources conservation, and environmental management policies should be carried out to search for sustainable solutions temporally and spatially with different scales under uncertainties. This study is aimed to develop an innovative, interdisciplinary, and insightful modeling framework to deal with global change issues as a whole based on a real-world drinking water infrastructure system expansion program in Manatee County, Florida. Four intertwined components within the drinking water infrastructure system planning were investigated and integrated, which consists of water demand analysis, GHG emission potential, system optimization for infrastructure expansion, and nested minimax-regret (NMMR) decision analysis under uncertainties. In the water demand analysis, a new system dynamics model was developed to reflect the intrinsic relationship between water demand and changing socioeconomic iv environment. This system dynamics model is based on a coupled modeling structure that takes the interactions among economic and social dimensions into account offering a satisfactory platform. In the evaluation of GHG emission potential, a life cycle assessment (LCA) is conducted to estimate the carbon footprint for all expansion alternatives for water supply. The result of this LCA study provides an extra dimension for decision makers to extract more effective adaptation strategies. Both water demand forecasting and GHG emission potential were deemed as the input information for system optimization when all alternatives are taken into account simultaneously. In the system optimization for infrastructure expansion, a multiobjective optimization model was formulated for providing the multitemporal optimal facility expansion strategies. With the aid of a multi-stage planning methodology over the partitioned time horizon, such a systems analysis has resulted in a full-scale screening and sequencing with respect to multiple competing objectives across a suite of management strategies. In the decision analysis under uncertainty, such a system optimization model was further developed as a unique NMMR programming model due to the uncertainties imposed by the real-world problem. The proposed NMMR algorithm was successfully applied for solving the real-world problem with a limited scale for the purpose of demonstration.

This dissertation aims to enhance our understanding of the experiences of surrogates (e.g., family, close friends) who make medical decisions for a loved one in the intensive care unit (ICU) after a cardiac arrest. Nearly 500,000 Americans experience a cardiac arrest annually; given high mortality (80%-90%), most surrogates become bereaved. For those who receive post-cardiac arrest care in an ICU, almost three in four surrogates make decisions to limit life-sustaining treatments. The burden of medical decision-making for a loved one has been well-documented and those who serve as surrogate decision-makers in the ICU are known to experience symptoms (e.g., depression, post-traumatic stress) for months after their loved one’s hospitalization. However, it is unknown to what extent decision-making experiences near a loved one’s end-of-life influence symptom burden among bereaved surrogates after cardiac arrest. Decisional conflict, uncertainty about which course of action to take, is reported by half of surrogates faced with ICU treatment decisions and one in five report regret around their decisions after 6 months. Following a cardiac arrest, prognostic uncertainty can complicate surrogate decision-making and potentially worsen decisional conflict and/or regret. The overall objective of this dissertation is to inform future interventions to improve outcomes for this highly vulnerable group. The dissertation study aims were to (1) evaluate the efficacy of interventions for ICU surrogates facing end-of-life decisions, (2) explore differences in surrogate decision-making experiences by level of decisional conflict reported around end-of-life decisions after cardiac arrest, (3) assess physical and psychological symptoms among surrogates during the first 6 months of bereavement after a loved one’s cardiac arrest, and (4) explore relationships between decisional conflict, decision regret, and symptoms. To address these aims, three studies were conducted. Study 1 was a systematic review and meta-analysis to evaluate the efficacy of interventions to improve symptoms among surrogates whose loved one had either died in the ICU or had high predicted likelihood of mortality. The study demonstrated that interventions have yielded only small, significant improvement in depression and post-traumatic stress at 3 months and anxiety at 6 months; findings derived from the meta-analysis have moderate-to-very-low certainty of evidence and have potentially limited clinical utility. Most interventions were delivered in the ICU, suggesting that different approaches (e.g., beyond the ICU) warrant exploration. Studies 2 and 3 report findings from a convergent mixed methods study of bereaved cardiac arrest surrogates. Study design was informed by the Integrative Risk Factor Framework for the Prediction of Bereavement Outcome which includes various inter- and intrapersonal risk factors in addition to bereavement-related stressors that influence outcomes such as symptoms. Surrogates were recruited and enrolled ~1-month after the death of their loved one and were followed through 6 months. Survey data were collected at ~1-, 2-, 3-, and 6-months. Most surrogates also completed interviews which were conducted at ~1-month and 3-months. Study 2 aimed to explore differences in surrogate decision-making experiences by decisional conflict reported around end-of-life decisions in the ICU. Among the 16 surrogates who completed both surveys and interviews at ~1-month, decisional conflict survey scores were relatively low with more than half reporting no decisional conflict. Three themes emerged from interview data, two related to decision-making experiences and one related to broader experiences during the first month after the loved one’s death. Compared to those who reported no decisional conflict, those who did described lack of clarity around their loved one’s preferences for treatment, less support from other family or clinicians, and a poorer understanding of medical treatments or prognosis. All surrogates described challenges navigating life after the loss. Qualitative data provided insight into limitations of retrospective assessment of decisional conflict, highlighted opportunities for enhanced measurement of the construct among surrogate decision-makers, and identified potential areas of focus for future interventions. Study 3 aimed to assess physical and psychological symptoms during the first 6 months of bereavement and explore relationships between decisional conflict, decision regret, and symptoms. Findings demonstrated that more than a third experienced high grief intensity and/or post-traumatic stress 6 months after medical decision-making. Strong correlations were seen between 1-month and 6-month symptoms (i.e., depression, post-traumatic stress, fatigue, sleep disturbance), suggesting that those with high symptom burden early on are likely to have symptoms that persist. Decisional conflict moderately correlated with decision regret at 6 months which moderately correlated with other psychological symptoms (i.e., anxiety, post-traumatic stress, grief intensity). The exploratory findings suggest that early screening may be helpful in identifying surrogates at highest risk for poor outcomes at 6 months and may help target future interventions towards those who need them most. This dissertation makes valuable contributions to our current understanding of the experiences of surrogate medical decision-making near a loved one’s end-of-life in the ICU after cardiac arrest and of surrogate experiences during bereavement. Chapter 5 summarizes each study, reviews key findings, identifies strengths and limitations, and discusses implications for future research, clinical practice, and health policy. Together, these studies support the need for enhanced care for surrogates bereaved after a loved one’s cardiac arrest/critical illness. Surrogates described the burden of medical decision-making near a loved one’s end-of-life in the ICU and the challenges encountered during bereavement. Findings suggest that end-of-life decision-making experiences may influence symptoms through the first 6 months of bereavement. Novel approaches to supporting surrogates are warranted to improve health outcomes for this important, vulnerable group.

Det senaste decenniet har användandet av sociala medier exploderat och blivit en plattformdär information och tips om aktier och investeringar delas ut. Unga personer är de störstaanvändarna av sociala medier, och tidigare studier visar att denna åldersgrupp uppvisar ettmer riskfyllt beteende på aktiemarknaden. Syftet med denna studie var således att undersökahuruvida det finns ett samband mellan aktivitet på sociala medier och riskbenägenhet. Vidareundersöktes om tre variabler - överdrivet självförtroende, ångeraversion och kognitivdissonans - hade en medierande effekt i sambandet mellan aktivitet på sociala medier ochriskbenägenhet. En kvantitativ metod med en enkätstudie användes för studiensdatainsamling. Statistiska mått, däribland regressionsanalys och medieringsanalys, användesför att besvara forskningsfrågan. Resultaten visade att sociala medier har en statistisktsignifikant effekt på riskbenägenhet på aktiemarknaden, och att överdrivet självförtroende haren statistiskt signifikant medierande effekt på relationen. Det fanns inga belägg ellerindikationer på att kognitiv dissonans och ångeraversion har en medierande effekt.Sammanfattningsvis visade studien att aktivitet på sociala medier i investeringssyfte kanbidra till ökad riskbenägenhet, och att överdrivet självförtroende har en viktig roll sommedierande variabel i förhållandet. / The last decade, the use of social media has escalated and become a platform whereinformation and tips about stocks and investments are shared. Young individuals aregenerally the most frequent users of social media, and studies also show that the same agegroup displays a more risk-prone behavior in financial markets. Therefore, the purpose of thisstudy was to examine the potential effect of social media activity on risk propensity on thestock market. Furthermore, the study investigated whether the three variables -overconfidence, regret aversion, and cognitive dissonance - could be classified as a mediatingvariable between social media activity and risk propensity. The study was conducted using aquantitative method, employing a survey, where 130 people responded. Statistical measuressuch as regression analysis and mediation analysis were used to answer the research question.The results showed that social media has a statistically significant effect on risk propensity onthe stock market, and that overconfidence has a statistically significant mediating effect onthe relationship. There was no evidence or indication that cognitive dissonance or regretaversion has a mediating effect. In summary, the study demonstrated that use of social mediain investment purposes can increase risk willingness, and that overconfidence plays animportant role as a mediating variable in this relationship.

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Le sujet de cette thèse porte sur la demande de pardon adressée officiellement par des gouvernements à des peuples ou à des groupes - souvent à une minorité de leur propre nation - victimes un jour de crimes, d'injustices ou d'atrocités. Il pose au départ plusieurs questions: d'où provient cette vague de demandes de pardon publiques et politiques, qui semble s'amplifier avec les années, et qui se répand aujourd'hui dans le monde entier? Quel crédit lui apporter? Quelle valeur peut avoir une demande de pardon venue du pouvoir, surtout quand elle est le résultat d'une exigence d'un peuple ou d'une collectivité? Peut-on réellement pardonner l'impardonnable, peut-on pardonner au nom des morts? Assiste-t-on à une simple mode, ou bien à un phénomène de réappropriation du politique par l'éthique? Pour répondre à ces questions, j'ai choisi de travailler sur le cas des Unangan (Aléoutes) de l'Alaska, qui, en 1988, reçurent du Congrès américain une demande de pardon officielle assortie de réparations financières, pour leur déportation et leur internement au cours de la Deuxième Guerre mondiale dans des conditions inhumaines. J'ai donc travaillé pendant six mois, au cours de l'année 2004, avec trois générations d'Unangan urbanisés à Anchorage, survivants de la déportation, enfants et petits-enfants. L'analyse de mes données montre d'abord que ces demandes de pardon officielles correspondent à la fois à une exigence des peuples en mal de reconnaissance, et à la fois à un nouveau courant de pensée morale qui traverse aujourd'hui nos sociétés. Elle montre d'autre part que, si elle veut passer le cap de la crédibilité, cette repentance politique suppose un certain nombre de conditions, qui caractérisent d'ordinaire le pardon interpersonnel: face à face, coeur à coeur, repentir, justice, réparations, engagement à se transformer et à ne plus répéter le même crime, etc. Elle montre enfin que la double aporie, représentée par le pardon de l'impardonnable et l'introduction d'une valeur pure dans le domaine du politique, auquel elle est a priori hétérogène sur tous les plans, peut être renversée, et donc vécue positivement. En conclusion, cette étude avance la théorie que les peuples un jour brisés et traumatisés peuvent à travers le pardon opérer un début de réconciliation, et que les demandes de pardon des États, même incomplètes et même imparfaites, parce qu'elles reconnaissent les crimes du passé et font avancer l'Histoire, apportent leur contribution à une meilleure humanité.

<p dir="ltr">Learning, planning, and representing knowledge at multiple levels of temporal abstractions provide an agent with the ability to predict consequences of different courses of actions, which is essential for improving the performance of sequential decision making. However, discovering effective temporal abstractions, which the agent can use as skills, and adopting the constructed temporal abstractions for efficient policy learning can be challenging. Despite significant advancements in single-agent settings, temporal abstractions in multi-agent systems remains underexplored. This thesis addresses this research gap by introducing novel algorithms for discovering and employing temporal abstractions in both cooperative and competitive multi-agent environments. We first develop an unsupervised spectral-analysis-based discovery algorithm, aiming at finding temporal abstractions that can enhance the joint exploration of agents in complex, unknown environments for goal-achieving tasks. Subsequently, we propose a variational method that is applicable for a broader range of collaborative multi-agent tasks. This method unifies dynamic grouping and automatic multi-agent temporal abstraction discovery, and can be seamlessly integrated into the commonly-used multi-agent reinforcement learning algorithms. Further, for competitive multi-agent zero-sum games, we develop an algorithm based on Counterfactual Regret Minimization, which enables agents to form and utilize strategic abstractions akin to routine moves in chess during strategy learning, supported by solid theoretical and empirical analyses. Collectively, these contributions not only advance the understanding of multi-agent temporal abstractions but also present practical algorithms for intricate multi-agent challenges, including control, planning, and decision-making in complex scenarios.</p>

Cette thèse s'inscrit dans le domaine de la prise de décision séquentielle en environnement inconnu, et plus particulièrement dans le cadre des bandits manchots (multi-armed bandits, MAB), défini par Robbins et Lai dans les années 50. Depuis les années 2000, ce cadre a fait l'objet de nombreuses recherches théoriques et algorithmiques centrées sur le compromis entre l'exploration et l'exploitation : L'exploitation consiste à répéter le plus souvent possible les choix qui se sont avérés les meilleurs jusqu'à présent. L'exploration consiste à essayer des choix qui ont rarement été essayés, pour vérifier qu'on a bien identifié les meilleurs choix. Les applications des approches MAB vont du choix des traitements médicaux à la recommandation dans le contexte du commerce électronique, en passant par la recherche de politiques optimales de l'énergie. Les contributions présentées dans ce manuscrit s'intéressent au compromis exploration vs exploitation sous deux angles spécifiques. Le premier concerne la prise en compte du risque. Toute exploration dans un contexte inconnu peut en effet aboutir à des conséquences indésirables ; par exemple l'exploration des comportements d'un robot peut aboutir à des dommages pour le robot ou pour son environnement. Dans ce contexte, l'objectif est d'obtenir un compromis entre exploration, exploitation, et prise de risque (EER). Plusieurs algorithmes originaux sont proposés dans le cadre du compromis EER. Sous des hypothèses fortes, l'algorithme MIN offre des garanties de regret logarithmique, à l'état de l'art ; il offre également une grande robustesse, contrastant avec la forte sensibilité aux valeurs des hyper-paramètres de e.g. (Auer et al. 2002). L'algorithme MARAB s'intéresse à un critère inspiré de la littérature économique(Conditional Value at Risk), et montre d'excellentes performances empiriques comparées à (Sani et al. 2012), mais sans garanties théoriques. Enfin, l'algorithme MARABOUT modifie l'estimation du critère CVaR pour obtenir des garanties théoriques, tout en obtenant un bon comportement empirique. Le second axe de recherche concerne le bandit contextuel, où l'on dispose d'informations additionnelles relatives au contexte de la décision ; par exemple, les variables d'état du patient dans un contexte médical ou de l'utilisateur dans un contexte de recommandation. L'étude se focalise sur le choix entre bras qu'on a tirés précédemment un nombre de fois différent. Le choix repose en général sur la notion d'optimisme, comparant les bornes supérieures des intervalles de confiance associés aux bras considérés. Une autre approche appelée BESA, reposant sur le sous-échantillonnage des valeurs tirées pour les bras les plus visités, et permettant ainsi de se ramener au cas où tous les bras ont été tirés un même nombre de fois, a été proposée par (Baransi et al. 2014). / This thesis focuses on sequential decision making in unknown environment, and more particularly on the Multi-Armed Bandit (MAB) setting, defined by Lai and Robbins in the 50s. During the last decade, many theoretical and algorithmic studies have been aimed at cthe exploration vs exploitation tradeoff at the core of MABs, where Exploitation is biased toward the best options visited so far while Exploration is biased toward options rarely visited, to enforce the discovery of the the true best choices. MAB applications range from medicine (the elicitation of the best prescriptions) to e-commerce (recommendations, advertisements) and optimal policies (e.g., in the energy domain). The contributions presented in this dissertation tackle the exploration vs exploitation dilemma under two angles. The first contribution is centered on risk avoidance. Exploration in unknown environments often has adverse effects: for instance exploratory trajectories of a robot can entail physical damages for the robot or its environment. We thus define the exploration vs exploitation vs safety (EES) tradeoff, and propose three new algorithms addressing the EES dilemma. Firstly and under strong assumptions, the MIN algorithm provides a robust behavior with guarantees of logarithmic regret, matching the state of the art with a high robustness w.r.t. hyper-parameter setting (as opposed to, e.g. UCB (Auer 2002)). Secondly, the MARAB algorithm aims at optimizing the cumulative 'Conditional Value at Risk' (CVar) rewards, originated from the economics domain, with excellent empirical performances compared to (Sani et al. 2012), though without any theoretical guarantees. Finally, the MARABOUT algorithm modifies the CVar estimation and yields both theoretical guarantees and a good empirical behavior. The second contribution concerns the contextual bandit setting, where additional informations are provided to support the decision making, such as the user details in the ontent recommendation domain, or the patient history in the medical domain. The study focuses on how to make a choice between two arms with different numbers of samples. Traditionally, a confidence region is derived for each arm based on the associated samples, and the 'Optimism in front of the unknown' principle implements the choice of the arm with maximal upper confidence bound. An alternative, pioneered by (Baransi et al. 2014), and called BESA, proceeds instead by subsampling without replacement the larger sample set. In this framework, we designed a contextual bandit algorithm based on sub-sampling without replacement, relaxing the (unrealistic) assumption that all arm reward distributions rely on the same parameter. The CL-BESA algorithm yields both theoretical guarantees of logarithmic regret and good empirical behavior.

Submitted by Sara Ribeiro (sara.ribeiro@ucb.br) on 2018-11-09T17:57:39Z No. of bitstreams: 1 OrlandoMaurizRamosDissertacao2018.pdf: 901886 bytes, checksum: 651204f0a4fd8e26d90341f87258fac2 (MD5) / Approved for entry into archive by Sara Ribeiro (sara.ribeiro@ucb.br) on 2018-11-13T15:56:26Z (GMT) No. of bitstreams: 1 OrlandoMaurizRamosDissertacao2018.pdf: 901886 bytes, checksum: 651204f0a4fd8e26d90341f87258fac2 (MD5) / Made available in DSpace on 2018-11-13T15:56:26Z (GMT). No. of bitstreams: 1 OrlandoMaurizRamosDissertacao2018.pdf: 901886 bytes, checksum: 651204f0a4fd8e26d90341f87258fac2 (MD5) Previous issue date: 2018-09-15 / The Principle of Equality should be used in all situations involving legal relationships. With the advent of Law no. 9249/95, and consequently with the possibility of extinguishing punishment of authors of crimes against the tax order, after the effective payment of the helpless taxes, some controversies arose regarding the coercive effectiveness of Criminal Law. However, it is observed a differentiated treatment of non-taxable offenders, hence the importance of analyzing the instituting of punishment and acquittals in another perspective. Given that the Brazilian prison population is large, mainly due to practices of crimes against the patrimony, it is searched with the present work, to analyze the fact of the equal application of the benefit given to the authors of the crimes against the tax order, also to the authors of other crimes, who may repent of the criminal practice, restoring the injured object or, in its impossibility, repairing, in a certain way, the damage caused. Equal treatment is proposed between offenders, observing the possibility of extinguishing punishment, with an eye towards reducing new criminal practices, as well as reducing the prison population, generating a possibility of saving for the state, since it will not be obliged to costing the maintenance of the prisoners, a benefit for the victim, since they will be compensated for the damage caused by the practice of the crime, and a possibility of a second chance for the perpetrator, who will not be incarcerated. The analysis was based on bibliographical research, having as sources the doctrine, technical productions and jurisprudences. At first, the importance of taxes was analyzed for the maintenance of state activities, conceptualizing and extracting the purpose of the taxes, in order to understand the need to classify crimes against the tax order, and consequent application of a penalty to the offender. In a second moment, it is sought to understand the beneficent institutes of the Later Regret (Later Repentance) and the Acquittal Excuse (Excusive Absence). And then, the possibility of equal treatment and possible benefits, with the application of the abovementioned institutes, against the State, the victim and the aggressor was evaluated. / O Princípio da Igualdade deverá ser utilizado em todas as situações que envolvam relações jurídicas. Com o advento da Lei nº9.249/95, e, consequentemente, com a possibilidade da extinção de punibilidade aos autores de crimes contra a ordem tributária, após o efetivo pagamento dos tributos sonegados, surgiram algumas controvérsias no tocante à eficácia coercitiva do Direito Penal. Contudo, observa-se um tratamento diferenciado para com os autores de infrações que não tenham cunho tributário, daí a importância da análise dos institutos da extinção de punibilidade e das escusas absolutórias, numa outra ótica. Dado que a população carcerária brasileira encontra-se vultuosa, principalmente devido a práticas de crimes contra o patrimônio, busca-se com o presente trabalho, analisar o fato da aplicação equiparada do benefício dado aos autores dos crimes contra a ordem tributária, também aos autores de outros crimes, que porventura venham a se arrepender da prática delituosa, restituindo o objeto lesado, ou, na sua impossibilidade, reparando, de certa forma, o dano causado. Propõem-se um tratamento igualitário entre os infratores, observando a possibilidade da extinção da punibilidade, com olhos voltados à redução de novas práticas delituosas, bem como na diminuição da população carcerária, gerando uma possibilidade de economia para o estado, pois não será obrigado a custear a manutenção dos presos, um benefício para a vítima, vez que será ressarcida do prejuízo causado pela prática do crime, e uma possibilidade de segunda chance para o autor, que não será encarcerado. A análise se fundamentou em pesquisas bibliográficas, tendo como fontes a doutrina, produções técnicas e jurisprudências. Num primeiro momento foi analisado a importância dos tributos para a manutenção das atividades estatais, conceituando e extraindo a finalidade dos tributos, para se entender a necessidade da tipificação de crimes contra a ordem tributária, e consequente aplicação de uma pena ao infrator. Num segundo momento busca-se entender os institutos benéficos do Arrependimento Posterior e da Escusa Absolutória. E em seguida foi avaliado a possibilidade do tratamento igualitário e eventuais benefícios, com a aplicação dos institutos acima mencionados, frente o Estado, a vítima e o agressor.

This dissertation studies models for locating facilities in time varying demand environments. We describe the characteristics of the time varying demand that motivate the analysis of our location models in terms of total demand and the change in value and location of the demand of each customer. The first part of the dissertation is devoted to the dynamic location model, which determines the optimal time and location for establishing capacitated facilities when demand and cost parameters are time varying. This model minimizes the total cost over a discrete and finite time horizon for establishing, operating, and closing facilities, including the transportation costs for shipping demand from facilities to customers. The model is solved using Lagrangian relaxation and Benders? decomposition. Computational results from different time varying total demand structures demonstrate, empirically, the performance of these solution methods. The second part of the dissertation studies two location models where relocation of facilities is not allowed and the objective is to determine the optimal location of capacitated facilities that will have a good performance when demand and cost parameters are time varying. The first model minimizes the total cost for opening and operating facilities and the associated transportation costs when demand and cost parameters are time varying. The model is solved using Benders? decomposition. We show that in the presence of high relocation costs of facilities (opening and closing costs), this model can be solved as a special case by the dynamic location model. The second model minimizes the maximum regret or opportunity loss between a robust configuration of facilities and the optimal configuration for each time period. We implement local search and simulated annealing metaheuristics to efficiently obtain near optimal solutions for this model.

We focus on the two overlapping areas of preference queries and dataset summarization. A (linear) preference query specifies the relative importance of the attributes in a dataset and asks for the tuples that best match those preferences. Dataset summarization is the task of representing an entire dataset by a small, representative subset. Within these areas, we focus on three important sub-problems, significantly advancing the state-of-the-art in each. We begin with an investigation into a new formulation of preference queries, identifying a neglected and important subclass that we call threshold projection queries. While literature typically constrains the attribute preferences (which are real-valued weights) such that their sum is one, we show that this introduces bias when querying by threshold rather than cardinality. Using projection, rather than inner product as in that literature, removes the bias. We then give algorithms for building and querying indices for this class of query, based, in the general case, on geometric duality and halfspace range searching, and, in an important special case, on stereographic projection. In the second part of the dissertation, we investigate the monochromatic reverse top-k (mRTOP) query in two dimensions. A mRTOP query asks for, given a tuple and a dataset, the linear preference queries on the dataset that will include the given tuple. Towards this goal, we consider the novel scenario of building an index to support mRTOP queries, using geometric duality and plane sweep. We show theoretically and empirically that the index is quick to build, small on disk, and very efficient at answering mRTOP queries. As a corollary to these efforts, we defined the top-k rank contour, which encodes the k-ranked tuple for every possible linear preference query. This is tremendously useful in answering mRTOP queries, but also, we posit, of significant independent interest for its relation to myriad related linear preference query problems. Intuitively, the top-k rank contour is the minimum possible representation of knowledge needed to identify the k-ranked tuple for any query, without apriori knowledge of that query. We also introduce k-regret minimizing sets, a very succinct approximation of a numeric dataset. The purpose of the approximation is to represent the entire dataset by just a small subset that nonetheless will contain a tuple within or near to the top-k for any linear preference query. We show that the problem of finding k-regret minimizing sets—and, indeed, the problem in literature that it generalizes—is NP-Hard. Still, for the special case of two dimensions, we provide a fast, exact algorithm based on the top-k rank contour. For arbitrary dimension, we introduce a novel greedy algorithm based on linear programming and randomization that does excellently in our empirical investigation. / Graduate / 0984