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Tsinghua Science and Technology  2019, Vol. 24 Issue (2): 171-182    doi: 10.26599/TST.2018.9010051
Computing Skyline Groups: An Experimental Evaluation
Haoyang Zhu, Xiaoyong Li*, Qiang Liu, Hao Zhu
∙ Haoyang Zhu is with the Academy of Military Science of the People’s Liberation Army, Beijing 100091, China. E-mail:
∙ Xiaoyong Li is with the Academy of Ocean Science and Engineering, National University of Defense Technology, Changsha 410073, China.
∙ Qiang Liu and Hao Zhu are with the College of Computer, National University of Defense Technology, Changsha 410073, China. E-mail:;
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Skyline group, also named as combinational skyline or group-based skyline, has attracted more attention recently. The concept of skyline groups is proposed to address the problem in the inadequacy of the traditional skyline to answer queries that need to analyze not only individual points but also groups of points. Skyline group algorithms aim at finding groups of points that are not dominated by any other same-size groups. Although two types of dominance relationship exist between the groups defined in existing works, they have not been compared systematically under the same experimental framework. Thus, practitioners face difficulty in selecting an appropriate definition. Furthermore, the experimental evaluation in most existing works features a weakness, that is, studies only experimented on small data sets or large data sets with small dimensions. For comprehensive comparisons of the two types of definition and existing algorithms, we evaluate each algorithm in terms of time and space on various synthetic and real data sets. We reveal the characteristics of existing algorithms and provide guidelines on selecting algorithms for different situations.

Key wordsskyline queries      skyline groups      performance evaluation     
Received: 22 May 2017      Published: 29 April 2019
Corresponding Authors: Xiaoyong Li   
About author:

Hao Zhu received the PhD degree in the SNE group from Delft University of technology, in 2015. Now he is a researcher in the College of Computer Science, National University of Defense Technology. His research interests are in the area of green computing and GPU computing. To be particular, he studies power estimation models, power management of heterogeneous system, and real time GPU computing.

Cite this article:

Haoyang Zhu, Xiaoyong Li, Qiang Liu, Hao Zhu. Computing Skyline Groups: An Experimental Evaluation. Tsinghua Science and Technology, 2019, 24(2): 171-182.

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Fig. 1 A skyline example.
Dd-dimensional data set
dNumber of dimensions
nNumber of points in D
QiThe i?-th point in D
QjiValue on the j?-th dimension of Qi
Preference/dominance relation
SkylineSkyline of data set D
lSize of a group
Table 1 Summary of notations.
Fig. 2 Dominance relations under different aggregate functions.
Skyline group
Table 2 Skyline groups under different definitions.
Fig. 3 An example of computing 2-point skyline groups under Permutation.
n l=2l=4l=6
4×105G258323120226825917523619×10511 757107681.52×108
V258284118259139635711 7571762
6×105G2481584120276025643983691.3×10615 145367422.79×108
V248300120256432136915 1451736
Table 3 G and V, under various n, l (d=6).
d l=2l=4l=6
4G19641116756701253751172283 155
5G65118356302456404775 6745911×108504.2×106
7G2857001774475321677236053.5×10618 541391212761.2×109
V2855371773216132060518 541991276
Table 4 G and V, under various d, l (n=1 ×?×𝟏𝟎𝟔).
Fig. 4 Runtime on NBA data set.
Fig. 5 Output size on NBA data set.
Fig. 6 Experimental results on NBA data set under MAX.
Fig. 7 Experimental results on NBA data set under MIN.
Fig. 8 (a) and (b): Runtime; (c) and (d): output size, mixture of SUM, MAX, and MIN.
Fig. 9 Experimental results on correlated data sets (n=1××𝟏𝟎𝟔,l=2).
Fig. 10 Experimental results on independent data sets (n=1××𝟏𝟎𝟔,l=2).
Fig. 11 Experimental results on anti-correlated data sets (n=1××𝟏𝟎𝟔,l=2).
Table 5 Characteristics of existing algorithms.
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