Skyline Operator on Anti-correlated Distributions

Finding the skyline in a multi-dimensional space is relevant to a wide range of applications. The skyline operator over a set of d-dimensional points selects the points that are not dominated by any other point on all dimensions. Therefore, it provides a minimal set of candidates for the users to make their personal trade-off among all optimal solutions. The existing algorithms establish both the worst case complexity by discarding distributions and the average case complexity by assuming dimensional independence. However, the data in the real world is more likely to be anti-correlated. The cardinality and complexity analysis on dimensionally independent data is meaningless when dealing with anti-correlated data. Furthermore, the performance of the existing algorithms becomes impractical on anti-correlated data. In this paper, we establish a cardinality model for anti-correlated distributions. We propose an accurate polynomial estimation for the expected value of the skyline cardinality. Because the high skyline cardinality downgrades the performance of most existing algorithms on anti-correlated data, we further develop a determination and elimination framework which extends the well-adopted elimination strategy. It achieves remarkable effectiveness and efficiency. The comprehensive experiments on both real datasets and benchmark synthetic datasets demonstrate that our approach significantly outperforms the state-of-the-art algorithms under a wide range of settings.