The skyline of a d-dimensional dataset contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive methods that can quickly return the initial results without reading the entire database. All the existing algorithms, however, have some serious shortcomings which limit their applicability in practice. In this article we develop branch-and-bound skyline (BBS), an algorithm based on nearest-neighbor search, which is I/O optimal, that is, it performs a single access only to those nodes that may contain skyline points. BBS is simple to implement and supports all types of progressive processing (e.g., user preferences, arbitrary dimensionality, etc). Furthermore, we propose several interesting variations of skyline computation, and show how BBS can be applied for their efficient processing.

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Progressive skyline computation in database systems

The skyline of a set of d-dimensional points contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive (or online) algorithms that can quickly return the first skyline points without having to read the entire data file. Currently, the most efficient algorithm is NN (nearest neighbors), which applies the divide -and-conquer framework on datasets indexed by R-trees. Although NN has some desirable features (such as high speed for returning the initial skyline points, applicability to arbitrary data distributions and dimensions), it also presents several inherent disadvantages (need for duplicate elimination if d>2, multiple accesses of the same node, large space overhead). In this paper we develop BBS (branch-and-bound skyline), a progressive algorithm also based on nearest neighbor search, which is IO optimal, i.e., it performs a single access only to those R-tree nodes that may contain skyline points. Furthermore, it does not retrieve duplicates and its space overhead is significantly smaller than that of NN. Finally, BBS is simple to implement and can be efficiently applied to a variety of alternative skyline queries. An analytical and experimental comparison shows that BBS outperforms NN (usually by orders of magnitude) under all problem instances.

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An optimal and progressive algorithm for skyline queries

The skyline, or Pareto, operator selects those tuples that are not dominated by any others. Extending relational systems with the skyline operator would offer a basis for handling preference queries. Good algorithms are needed for skyline, however, to make this efficient in a relational setting. We propose a skyline algorithm, SFS, based on presorting that is general, for use with any skyline query, efficient, and well behaved in a relational setting.

Skyline with presorting

Uncertain data are inherent in some important applications. Although a considerable amount of research has been dedicated to modeling uncertain data and answering some types of queries on uncertain data, how to conduct advanced analysis on uncertain data remains an open problem at large. In this paper, we tackle the problem of skyline analysis on uncertain data. We propose a novel probabilistic skyline model where an uncertain object may take a probability to be in the skyline, and a p-skyline contains all the objects whose skyline probabilities are at least p. Computing probabilistic skylines on large uncertain data sets is challenging. We develop two efficient algorithms. The bottom-up algorithm computes the skyline probabilities of some selected instances of uncertain objects, and uses those instances to prune other instances and uncertain objects effectively. The top-down algorithm recursively partitions the instances of uncertain objects into subsets, and prunes subsets and objects aggressively. Our experimental results on both the real NBA player data set and the benchmark synthetic data sets show that probabilistic skylines are interesting and useful, and our two algorithms are efficient on large data sets, and complementary to each other in performance.

/pdf/probabilistic-skylines-on-uncertain-data-1pd5isqdve.pdf

Probabilistic skylines on uncertain data

The handling of user preferences is becoming an increasingly important issue in present-day information systems. Among others, preferences are used for information filtering and extraction to reduce the volume of data presented to the user. They are also used to keep track of user profiles and formulate policies to improve and automate decision making.We propose here a simple, logical framework for formulating preferences as preference formulas. The framework does not impose any restrictions on the preference relations, and allows arbitrary operation and predicate signatures in preference formulas. It also makes the composition of preference relations straightforward. We propose a simple, natural embedding of preference formulas into relational algebra (and SQL) through a single winnow operator parameterized by a preference formula. The embedding makes possible the formulation of complex preference queries, for example, involving aggregation, by piggybacking on existing SQL constructs. It also leads in a natural way to the definition of further, preference-related concepts like ranking. Finally, we present general algebraic laws governing the winnow operator and its interactions with other relational algebra operators. The preconditions on the applicability of the laws are captured by logical formulas. The laws provide a formal foundation for the algebraic optimization of preference queries. We demonstrate the usefulness of our approach through numerous examples.

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Preference formulas in relational queries

Skyline queries ask for a set of interesting points from a potentially large set of data points. If we are traveling, for instance, a restaurant might be interesting if there is no other restaurant which is nearer, cheaper, and has better food. Skyline queries retrieve all such interesting restaurants so that the user can choose the most promising one. In this paper, we present a new online algorithm that computes the Skyline. Unlike most existing algorithms that compute the Skyline in a batch, this algorithm returns the first results immediately, produces more and more results continuously, and allows the user to give preferences during the running time of the algorithm so that the user can control what kind of results are produced next (e.g., rather cheap or rather near restaurants).

/pdf/shooting-stars-in-the-sky-an-online-algorithm-for-skyline-4rx1em92uh.pdf

Shooting stars in the sky: an online algorithm for skyline queries

We present a platform for Web services. Web services are implemented in a special XML programming language called XL [1, 2]. A Web service receives an XML message as input and returns an XML message as output. The platform supports a number of features that are particularly useful to implement Web services; e.g., logging, timetables, conversations, workflow management, automatic transactions, security. Our platform is going to be compliant with all W3C standards and emerging proposals. The programming language is very abstract and can be optimized automatically (like SQL). Furthermore, the platform allows to integrate Web services that are written in XL and other programming languages.

http://cidrdb.org/cidr2003/program/p8.pdf

Steffen Rost

Papers

Shooting stars in the sky: an online algorithm for skyline queries

XL: a platform for web services