Database users can be frustrated by having an empty answer to a query. In this paper, we propose a framework to systematically relax queries involving joins and selections. When considering relaxing a query condition, intuitively one seeks the ’minimal ’ amount of relaxation that yields an answer. We first characterize the types of answers that we return to relaxed queries. We then propose a lattice based framework in order to aid query relaxation. Nodes in the lattice correspond to different ways to relax queries. We characterize the properties of relaxation at each node and present algorithms to compute the corresponding answer. We then discuss how to traverse this lattice in a way that a non-empty query answer is obtained with the minimum amount of query condition relaxation. We implemented this framework and we present our results of a thorough performance evaluation using real and synthetic data. Our results indicate the practical utility of our framework. 1.

Unlike numerical preferences, preferences on attribute values do not show an inherent total order, but skyline computation has to rely on partial orderings explicitly stated by the user. In such orders many object values are incomparable, hence skylines sizes become unpractical. However, the Pareto semantics can be modified to benefit from indifferences: skyline result sizes can be essentially reduced by allowing the user to declare some incomparable values as equally desirable. A major problem of adding such equivalences is that they may result in intransitivity of the aggregated Pareto order and thus efficient query processing is hampered. In this paper we analyze how far the strict Pareto semantics can be relaxed while always retaining transitivity of the induced Pareto aggregation. Extensive practical tests show that skyline sizes can indeed be reduced about two orders of magnitude when using the maximum possible relaxation still guaranteeing the consistency with all user preferences.

Querying databases with preferences is an important research problem. Among various approaches to querying with preferences, the skyline framework is one of the most popular. A well known deficiency of that framework is that all attributes are of the same importance in skyline preference relations. Consequently, the size of the results of skyline queries may grow exponentially with the number of skyline attributes. Here we propose the framework called p-skylines which enriches skylines with the notion of attribute importance. It turns out that incorporating relative attribute importance in skylines allows for reduction in the corresponding query result sizes. We propose an approach to discovering importance relationships of attributes, based on user-selected sets of superior and inferior examples. We show that the problem of checking the existence of and the problem of computing an optimal p-skyline preference relation covering a given set of examples are NP-complete and FNP-complete, respectively. However, we also show that a restricted version of the discovery problem – using only superior examples to discover attribute importance – can be solved efficiently in polynomial time. Our experiments show that the proposed importance discovery algorithm has high accuracy and good scalability. 1.

Skylines with partial order preference semantics often result in huge answer sets and what is worse, they cannot be computed efficiently. In this paper we will explore the evaluation of so-called restricted skyline queries with partial order preferences under the paradigm of weak Pareto dominance. Weak Pareto dominance removes all objects from skylines, which are dominated by other objects in some query predicates, but in turn do not dominate these objects in any predicate. We will argue that this paradigm yields intuitive results, prove that it leads to lean sizes of the restricted skyline and show how it opens up the use of efficient algorithms for evaluation adopting the iteration of ranked result lists for each query predicate.

Deeply personalized database applications require intuitive and powerful preference query languages like Preference SQL, employing preference constructors that are closed under strict partial order semantics. However, sophisticated preference query optimization and efficient evaluation techniques are essential for a large-scale and successful practical use. In this paper we focus on the evaluation of an important class of Pareto preference queries that frequently occur in practice, a subset of which are the well-known skyline queries. Our new algorithm, called BNL ++, succeeds in considerably speeding up the usual block-nested loop (BNL) algorithm. In fact, a careful analysis of the underlying ‘better-than ’ graph enables us to identify new and effective pruning conditions. The applicability of BNL ++ also covers complex situations, where existing index-based evaluation algorithms cannot be used. At this stage BNL ++ is preliminary work. The next step will be to evaluate the performance of BNL ++ with a large practical e-commerce use case. 1

Skyline queries have recently received a lot of attention due to their intuitive query formulation: users can state preferences with respect to several attributes. Unlike numerical preferences, preferences over discrete value domains do not show an inherent total order, but have to rely on partial orders as stated by the user. In such orders typically many object values are incomparable, increasing the size of skyline sets significantly, and making their computation expensive. In this paper we explore how to enable interactive tasks like query refinement or relevance feedback by providing ‘prime cuts’. Prime cuts are interesting subsets of the full Pareto skyline, which give users a good overview over the skyline. They have to be small, efficient to compute, suitable for higher numbers of query predicates, and representative. The key to improved performance and reduced result set sizes is the relaxation of Pareto semantics to the concept of weak Pareto dominance. We argue that this relaxation yields intuitive results and show how it opens up the use of efficient and scalable query processing algorithms. Assessing the practical impact, our experiments show that our approach leads to lean result set sizes and outperforms Pareto skyline computations by up to two orders of magnitude.

Abstract. Networks of cooperating peers are a new exciting paradigm for evaluating queries in a distributed environment. In this scenario, a query originated at a peer propagates through the network, and the overall result is obtained by aggregating those returned by the peers involved in the evaluation. In this paper we consider the relevant case of preference queries, in which the user is interested in obtaining all and only the “best ” results. We highlight the fundamental difference between queries in which preferences define a weak order (wo) over objects and the more general ones for which a strict partial order (spo) hastobe considered. While for wo queries a simple algorithm that minimizes the overall number of objects to be transmitted across the network can be easily derived, we show that this is not the case for spo queries. Then, we detail a set of basic issues whose solution is a key to the derivation of an efficient distributed algorithm. 1

Abstract: Personalization includes the adaptation of database queries according to the user’s needs, wishes and situation. We examine the influence of the dparameter as powerful personalization instrument for the Preference XPath search engine. Using a heuristic approach we present a possibility to deliver not only the qualitative best matching objects but also the desired amount of data to the user. Performing a series of test queries on proper e-catalog data, we demonstrate the effectiveness of our approach. 1

Database queries expressing user preferences have been found to be crucial for personalized applications. Such preference queries, in particular Pareto preference queries, pose new optimization challenges for efficient evaluation. So far however, all known generic Pareto evaluation algorithms suffer from non-linear worst case runtimes. Here we present the first generic algorithm, called Hexagon, with linear worst case complexity for any data distribution under certain reasonable assumptions. In addition, our performance investigations provide evidence that Hexagon also beats competing Block-Nested-Loop style algorithms in the average case. Therefore Hexagon has the potential to become one key algorithm in each preference query optimizer’s repertoire. 1.

Nowadays, the efficient integration of preference querying into standard database technology is an important issue. In some instances, preference queries challenge traditional query processing and optimization. In this paper we study preference database queries involving hard constraints over multiple attributes belonging to several relations. The main bottleneck for such queries is the computation of the cartesian product which may lead to high memory and computation costs. We develop algebraic optimization techniques to transform a preference query with hard constraints in order to enable its efficient processing by database engines. For this purpose, we show a dominance criterion and we introduce rewriting techniques to eliminate dominated tuples before building the cartesian product and therefore speed up the evaluation. These techniques lead to novel preference transformation laws and extend previous developed rules. 1.