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5.7 Bibliographic Notes 241

iceberg cube computation method that factorizes the lattice space was developed by
Shao, Han, and Xin [SHX04]. The shell-fragment-based cubing approach for efficient
high-dimensional OLAP was proposed by Li, Han, and Gonzalez [LHG04].
Aside from computing iceberg cubes, another way to reduce data cube computa-
tion is to materialize condensed, dwarf, or quotient cubes, which are variants of closed
cubes. Wang, Feng, Lu, and Yu proposed computing a reduced data cube, called a con-
densed cube [WLFY02]. Sismanis, Deligiannakis, Roussopoulos, and Kotids proposed
computing a compressed data cube, called a dwarf cube [SDRK02]. Lakeshmanan,
Pei, and Han proposed a quotient cube structure to summarize a data cube’s seman-
tics [LPH02], which has been further extended to a qc-tree structure by Lakshmanan,
Pei, and Zhao [LPZ03]. An aggregation-based approach, called C-Cubing (i.e., Closed-
Cubing), has been developed by Xin, Han, Shao, and Liu [XHSL06], which performs
efficient closed-cube computation by taking advantage of a new algebraic measure
closedness.
There are also various studies on the computation of compressed data cubes by
approximation, such as quasi-cubes by Barbara and Sullivan [BS97]; wavelet cubes by
Vitter, Wang, and Iyer [VWI98]; compressed cubes for query approximation on continu-
ous dimensions by Shanmugasundaram, Fayyad, and Bradley [SFB99]; using log-linear
models to compress data cubes by Barbara and Wu [BW00]; and OLAP over uncertain
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and imprecise data by Burdick, Deshpande, Jayram, et al. [BDJ 05].
For works regarding the selection of materialized cuboids for efficient OLAP query
processing, see Chaudhuri and Dayal [CD97]; Harinarayan, Rajaraman, and Ullman
[HRU96]; Srivastava, Dar, Jagadish, and Levy [SDJL96]; Gupta [Gup97], Baralis,
Paraboschi, and Teniente [BPT97]; and Shukla, Deshpande, and Naughton [SDN98].
Methods for cube size estimation can be found in Deshpande, Naughton, Ramasamy,
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et al. [DNR 97], Ross and Srivastava [RS97], and Beyer and Ramakrishnan [BR99].
Agrawal, Gupta, and Sarawagi [AGS97] proposed operations for modeling multidimen-
sional databases.
Data cube modeling and computation have been extended well beyond relational
data. Computation of stream cubes for multidimensional stream data analysis has been
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studied by Chen, Dong, Han, et al. [CDH 02]. Efficient computation of spatial data
cubes was examined by Stefanovic, Han, and Koperski [SHK00], efficient OLAP in spa-
tial data warehouses was studied by Papadias, Kalnis, Zhang, and Tao [PKZT01], and a
map cube for visualizing spatial data warehouses was proposed by Shekhar, Lu, Tan, et al.
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[SLT 01]. A multimedia data cube was constructed in MultiMediaMiner by Zaiane,
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Han, Li, et al. [ZHL 98]. For analysis of multidimensional text databases, TextCube,
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based on the vector space model, was proposed by Lin, Ding, Han, et al. [LDH 08],
and TopicCube, based on a topic modeling approach, was proposed by Zhang, Zhai, and
Han [ZZH09]. RFID Cube and FlowCube for analyzing RFID data were proposed by
Gonzalez, Han, Li, et al. [GHLK06, GHL06].
The sampling cube was introduced for analyzing sampling data by Li, Han, Yin, et al.
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[LHY 08]. The ranking cube was proposed by Xin, Han, Cheng, and Li [XHCL06]
for efficient processing of ranking (top-k) queries in databases. This methodology has
been extended by Wu, Xin, and Han [WXH08] to ARCube, which supports the ranking
of aggregate queries in partially materialized data cubes. It has also been extended by