Efficient and Adaptive Skyline Computation Open Access

Liu, Jinfei (2017)

Permanent URL: https://etd.library.emory.edu/concern/etds/3j333309j?locale=en
Published

Abstract

Skyline, also known as Maxima in computational geometry or Pareto in business management field, is important for many applications involving multi-criteria decision making. The skyline of a set of multi-dimensional data points consists of the points for which no other point exists that is better in at least one dimension and at least as good in every other dimension. Although skyline computation and queries have been extensively studied in both computational geometry and database communities, there are still many challenges need to be fixed, especially in this big data era. In this dissertation, we present several efficient and adaptive skyline computation algorithms. First, we show a faster output-sensitive skyline computation algorithm which is the state-of-the-art algorithm from the theoretical aspect. Second, traditional skyline computation is inadequate to answer queries that need to analyze not only individual points but also groups of points. To address this gap, we adapt the original skyline definition to the novel group-based skyline (G-Skyline), which represents Pareto optimal groups that are not dominated by other groups. Third, to facilitate skyline queries, we propose a novel concept Skyline Diagram, which given a set of points, partitions the plane into a set of regions, referred to as skyline polyominos. Similar to kth-order Voronoi Diagram commonly used to facilitate k nearest neighbor (kNN) queries, any query points in the same skyline polyomino have the same skyline query results.

Table of Contents

1 Introduction 1

2 Faster Output-sensitive Skyline Computation 5 2.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Output-Sensitive Skyline Computation Algorithm . . . . . . . . 6 2.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Group-based Skyline 11 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 G-Skyline Definitions . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Constructing Directed Skyline Graph . . . . . . . . . . . . . . . 25 3.5 Finding G-Skyline Groups . . . . . . . . . . . . . . . . . . . . . 29 3.5.1 The Point-Wise Algorithm . . . . . . . . . . . . . . . . . 30 3.5.2 The Unit Group-Wise Algorithm . . . . . . . . . . . . . 34 3.6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.6.1 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . 38 3.6.2 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.6.3 Computing Skyline Layers . . . . . . . . . . . . . . . . . 40 3.6.4 G-Skyline Groups in the Synthetic Data . . . . . . . . . 42 3.6.5 G-Skyline Groups in the NBA Data . . . . . . . . . . . . 44 3.7 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.7.1 AG-Skyline . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.7.2 PG-Skyline . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4 Skyline Diagram 51 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.3 Preliminaries and Problem Definitions . . . . . . . . . . . . . . 60 4.4 Skyline Diagram of Quadrant and Global Skyline . . . . . . . . 63 4.4.1 Baseline Algorithm . . . . . . . . . . . . . . . . . . . . . 64 4.4.2 Directed Skyline Graph Algorithm . . . . . . . . . . . . 66 4.4.3 Scanning Algorithm . . . . . . . . . . . . . . . . . . . . . 69 4.4.4 Aggressive Scanning Algorithm . . . . . . . . . . . . . . 73 4.4.5 Skyline Diagram of Global Skyline . . . . . . . . . . . . 77 4.5 Skyline Diagram of Dynamic Skyline . . . . . . . . . . . . . . . 78 4.5.1 Baseline Algorithm . . . . . . . . . . . . . . . . . . . . . 78 4.5.2 Subset Algorithm . . . . . . . . . . . . . . . . . . . . . . 81 4.5.3 Scanning Algorithm . . . . . . . . . . . . . . . . . . . . . 81 4.6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.6.1 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . 84 4.6.2 Skyline Diagram of Quadrant Skyline . . . . . . . . . . . 85 4.6.3 Skyline Diagram of Global Skyline . . . . . . . . . . . . 87 4.6.4 Skyline Diagram of Dynamic Skyline . . . . . . . . . . . 88 4.6.5 Performance Improvements through Parallel Implementation. . . . . 89 4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5 Conclusion and Future Directions 91

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