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.