The VLDB Journal

, Volume 28, Issue 5, pp 675–701 | Cite as

Efficient two-dimensional Haar\(^+\) synopsis construction for the maximum absolute error measure

  • Jinhyun Kim
  • Jun-Ki MinEmail author
  • Kyuseok Shim
Regular Paper


Several wavelet synopsis construction algorithms were previously proposed for optimal Haar\(^+\) synopses. Recently, we proposed the OptExtHP-EB algorithm to find an optimal one-dimensional \(\hbox {Haar}^+\) synopsis. By utilizing the novel properties of optimal synopses, OptExtHP-EB represents the set of optimal synopses in a node of a \(\hbox {Haar}^+\) tree by a set of extended synopses. While it is much faster than the previous \(\hbox {Haar}^+\) synopsis construction algorithms, it can handle only one-dimensional data. In this paper, we propose the OptExtHP-EB2D algorithm for two-dimensional \(\hbox {Haar}^+\) synopses by extending OptExtHP-EB. While a one-dimensional \(\hbox {Haar}^+\) tree has only two child nodes and three coefficients in a node, a two-dimensional \(\hbox {Haar}^+\) tree is much more complex in that it has four child nodes and seven coefficients per node. Thus, for each possible subset of the coefficients selected in a node, we develop the efficient methods to compute a set of optimal synopses denoted by extended synopses. Our experiments confirm the effectiveness of our proposed OptExtHP-EB2D algorithm.


Query processing Data synopses Optimal wavelet synopsis construction Approximate query answering 



This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A02937186) as well as Next-Generation Information Computing Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT (NRF-2017M3C4A7063570). It was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT (NRF-2019R1F1A1062511).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Seoul National UniversitySeoulKorea
  2. 2.Korea University of Technology and EducationCheonanKorea

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