Over the last four decades, relational database systems, with their mathematical basis in first-order logic, have provided a congenial and efficient environment to handle enterprise data during its entire life cycle of generation, storage, maintenance and processing. An organic reason for their pervasive popularity is intrinsic support for declarative user queries, wherein the user only specifies the end objectives, and the system takes on the responsibility of identifying the most efficient means, called “plans”, to achieve these objectives. A crucial input to generating efficient query execution plans are the compile-time estimates of the data volumes that are output by the operators implementing the algebraic predicates present in the query. These volume estimates are typically computed using the “selectivities” of the predicates. Unfortunately, a pervasive problem encountered in practice is that these selectivities often differ significantly from the values actually encountered during query execution, leading to poor plan choices and grossly inflated response times. While the database research community has spent considerable efforts to address the above challenge, the prior techniques all suffer from a systemic limitation - the inability to provide any guarantees on the execution performance. In this thesis, we materially address this long-standing open problem by developing a radically different query processing strategy that lends itself to attractive guarantees on run-time performance. Specifically, in our approach, the compile-time estimation process is completely eschewed for error-prone selectivities. Instead, from the set of optimal plans in the query’s selectivity error space, a limited subset called the “plan bouquet”, is selected such that at least one of the bouquet plans is 2-optimal at each location in the space. Then, at run time, an exploratory sequence of cost-budgeted executions from the plan bouquet is carried out, eventually finding a plan that executes to completion within its assigned budget. The duration and switching of these executions is controlled by a graded progression of isosurfaces projected onto the optimal performance profile. We prove that this construction provides viable guarantees on the worst-case performance relative to an oracular system that magically possesses accurate apriori knowledge of all selectivities. Moreover, it ensures repeatable execution strategies across different invocations of a query, an extremely desirable feature in industrial settings. Our second contribution is a suite of techniques that substantively improve on the performance guarantees offered by the basic bouquet algorithm. First, we present an algorithm that skips carefully chosen executions from the basic plan bouquet sequence, leveraging the observation that an expensive execution may provide better coverage as compared to a series of cheaper siblings, thereby reducing the aggregate exploratory overheads. Next, we explore randomized variants with regard to both the sequence of plan executions and the constitution of the plan bouquet, and show that the resulting guarantees are markedly superior, in expectation, to the corresponding worst case values. From a deployment perspective, the above techniques are appealing since they are completely “black-box”, that is, non-invasive with regard to the database engine, implementable using only API features that are commonly available in modern systems. As a proof of concept, the bouquet approach has been fully prototyped in QUEST, a Java-based tool that provides a visual and interactive demonstration of the bouquet identification and execution phases. In similar spirit, we propose an efficient isosurface identification algorithm that avoids exploration of large portions of the error space and drastically reduces the effort involved in bouquet construction. The plan bouquet approach is ideally suited for “canned” query environments, where the computational investment in bouquet identification is amortized over multiple query invocations. The final contribution of this thesis is extending the advantage of compile-time sub-optimality guarantees to ad hoc query environments where the overheads of the off-line bouquet identification may turn out to be impractical. Specifically, we propose a completely revamped bouquet algorithm that constructs the cost-budgeted execution sequence in an “on-the-fly” manner. This is achieved through a “white-box” interaction style with the engine, whereby the plan output cardinalities exposed by the engine are used to compute lower bounds on the error-prone selectivities during plan executions. For this algorithm, the sub-optimality guarantees are in the form of a low order polynomial of the number of error-prone selectivities in the query. The plan bouquet approach has been empirically evaluated on both PostgreSQL and a commercial engine ComOpt, over the TPC-H and TPC-DS benchmark environments. Our experimental results indicate that it delivers orders of magnitude improvements in the worst-case behavior, without impairing the average-case performance, as compared to the native optimizers of these systems. In absolute terms, the worst case sub-optimality is upper bounded by 20 across the suite of queries, and the average performance is empirically found to be within a factor of 4 wrt the optimal. Even with the on-the-fly bouquet algorithm, the guarantees are found to be within a factor of 3 as compared to those achievable in the corresponding canned query environment. Overall, the plan bouquet approach provides novel performance guarantees that open up exciting possibilities for robust query processing.

Tous les problèmes définissables en logique du second ordre monadique peuvent être résolus en temps polynomial dans les classes de graphes qui ont une largeur de clique bornée. La largeur de clique est un paramètre de graphe défini de manière algébrique, c'est-à-dire, à partir d'opérations de composition de graphes. La largeur de rang, définie de manière combinatoire, est une notion équivalente à la largeur de clique des graphes non orientés. Nous donnons une caractérisation algébrique de la largeur de rang et nous montrons qu'elle est linéairement bornée par la largeur arborescente. Nous proposons également une notion de largeur de rang pour les graphes orientés et une relation de vertex-minor pour les graphes orientés. Nous montrons que les graphes orientés qui ont une largeur de rang bornée sont caractérisés par une liste finie de graphes orientés à exclure comme vertex-minor. Beaucoup de classes de graphes n'ont pas une largeur de rang bornée, par exemple, les graphes planaires. Nous nous intéressons aux systèmes d'étiquetage dans ces classes de graphes. Un système d'étiquetage pour une propriété P dans un graphe G, consiste à assigner une étiquette, aussi petite que possible, à chaque sommet de telle sorte que l'on puisse vérifier si G satisfait P en n'utilisant que les étiquettes des sommets. Nous montrons que si P est une propriété définissable en logique du premier ordre alors, certaines classes de graphes de largeur de clique localement bornée admettent un système d'étiquetage pour P avec des étiquettes de taille logarithmique. Parmi ces classes on peut citer les classes de graphes de degré borné, les graphes planaires et plus généralement les classes de graphes qui excluent un apex comme mineur et, les graphes d'intervalle unitaire. Si x et y sont deux sommets, X un ensemble de sommets et F un ensemble d'arêtes, nous notons Conn(x,y,X,F) la propriété qui vérifie dans un graphe donné si x et y sont connectés par un chemin, qui ne passe par aucun sommet de X si aucune arête de F. Cette propriété n'est pas définissable en logique du premier ordre. Nous montrons qu'elle admet un système d'étiquetage avec des étiquettes de taille logarithmique dans les graphes planaires. Nous montrons enfin que Conn(x,y,X,0) admet également un système d'étiquetage avec des étiquettes de taille logarithmique dans des classes de graphes qui sont définies comme des combinaisons de graphes qui ont une petite largeur de clique et telles que le graphe d'intersection de ces derniers est planaire et est de degré borné. / Every property definable in onadic second order logic can be checked in polynomial-time on graph classes of bounded clique-width. Clique-width is a graph parameter defined in an algebraical way, i.e., with operations ``concatenating graphs'' and that generalize concatenation of words.Rank-width, defined in a combinatorial way, is equivalent to the clique-width of undirected graphs. We give an algebraic characterization of rank-width and we show that rank-width is linearly bounded in term of tree-width. We also propose a notion of ``rank-width'' of directed graphs and a vertex-minor inclusion for directed graphs. We show that directed graphs of bounded ``rank-width'' are characterized by a finite list of finite directed graphs to exclude as vertex-minor. Many graph classes do not have bounded rank-width, e.g., planar graphs. We are interested in labeling schemes on these graph classes. A labeling scheme for a property P in a graph G consists in assigning a label, as short as possible, to each vertex of G and such that we can verify if G satisfies P by just looking at the labels. We show that every property definable in first order logic admit labeling schemes with labels of logarithmic size on certain graph classes that have bounded local clique-width. Bounded degree graph classes, minor closed classes of graphs that exclude an apex graph as a minor have bounded local clique-width. If x and y are two vertices and X is a subset of the set of vertices and Y is a subset of the set of edges, we let Conn(x,y,X,Y) be the graph property x and y are connected by a path that avoids the vertices in X and the edges in Y. This property is not definable by a first order formula. We show that it admits a labeling scheme with labels of logarithmic size on planar graphs. We also show that Conn(x,y,X,0) admits short labeling schemes with labels of logarithmic size on graph classes that are ``planar gluings'' of graphs of small clique-width and with limited overlaps.

Recently, multi-priced timed automata have received much attention for real-time systems. These automata extend priced timed automata by featuring several price parameters. This permits to compute objectives like the optimal ratio between rewards and costs. Arising from the model of timed automata, the multi-weighted setting has also attracted much notice for classical nondeterministic automata. The present thesis develops multi-weighted MSO-logics on finite, infinite and timed words which are expressively equivalent to multi-weighted automata, and studies decision problems for them. In addition, a Nivat-like theorem for weighted timed automata is proved; this theorem establishes a connection between quantitative and qualitative behaviors of timed automata. Moreover, a logical characterization of timed pushdown automata is given.