Efficient two-dimensional Haar+ synopsis construction for the maximum absolute error measure

• Published in: The VLDB journal Vol. 28; no. 5; pp. 675 - 701
• Main Authors: Kim, Jinhyun, Min, Jun-Ki, Shim, Kyuseok
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2019; Springer Nature B.V
• Subjects: Algorithms; Coefficients; Computer Science; Database Management; Error analysis; Nodes; Regular Paper; Wavelet analysis; Approximate query answering; Data synopses; Query processing; Optimal wavelet synopsis construction
• ISSN: 1066-8888; 0949-877X
• DOI: 10.1007/s00778-019-00551-2

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 Haar + synopsis. By utilizing the novel properties of optimal synopses, OptExtHP-EB represents the set of optimal synopses in a node of a Haar + tree by a set of extended synopses. While it is much faster than the previous Haar + synopsis construction algorithms, it can handle only one-dimensional data. In this paper, we propose the OptExtHP-EB2D algorithm for two-dimensional Haar + synopses by extending OptExtHP-EB. While a one-dimensional Haar + tree has only two child nodes and three coefficients in a node, a two-dimensional 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.