Generic Analysis and Methods for Computing Skyline Variants

Skyline queries are often used on data sets in multi-dimensional space for many decision-making applications. Traditionally, a point p is said to dominate another point q if, for all dimension, it is no worse than q and is better on at least one dimension. Therefore, the skyline of a data set consists of all points not dominated by any other point. To better cater to application requirements such as controlling the size of the skyline or handling data sets that are not well-structured, various works have been proposed to extend the definition of skyline based on variants of the dominance relationship. However, it is difficult to implement each of these variants separately in a system setting and instead effort must be made to provide a general framework so that these specific implementations can be easily materialized over the framework. Zhenjie Zhang Department of Computer Science School of Computing National University of Singapore E-mail: [email protected] Hua Lu Department of Computer Science Faculties of Engineering, Science, and Medicine Aalborg University E-mail: [email protected] Beng Chin Ooi Department of Computer Science School of Computing National University of Singapore E-mail: [email protected] Anthony K. H. Tung Department of Computer Science School of Computing National University of Singapore E-mail: [email protected] In this paper, a generalized framework is proposed for this purpose. Our framework explicitly and carefully examines the various properties that should be preserved in a variant of the dominance relationship so that: (1) the original advantages of skyline can be maintained while adaptivity to application semantics is also catered to and (2) computational complexity is almost unaffected. We prove that traditional dominance is the only relationship satisfying all desirable properties and present some new dominance relationships to illustrate that other skyline variants always have their tradeoff in relaxing some of the properties. We then developed generic algorithms that compute skyline variants subject to the constraints that certain properties are relaxed and illustrate the use of our framework in computing of skyline over datasets with missing values. Extensive experimental results are presented to evaluate the efficiency and effectiveness of our framework.