Compression Schemes of High Dimensional Data for MOLAP - Evolving Application Domains of Data Warehousing and Mining - page 68

Figure 2. Multidimensional array chunking

The logical position (i.e. offset value) is calcu-
lated for the records using the forward mapping
function F and stored on a data structure (Hasan
et, al; 2007) along with the measure value. The
backward mapping algorithm R-F is used to
determine the coordinates of the corresponding
multidimensional array.

Chunk 16 is itself 4×2×3 array whose 24 cells
are numbered in row-major order and are stored
contiguously (Owen, 2002).
In chunk-offset compression, for each valid ar-
ray entry, a pair (OffsetInChunk, data) is stored.
The offset inside the chunk (OffsetInChunk)
can be computed using the multidimensional ar-
ray linearization function described before. The
reverse array linearization function is used for
backward mapping to get the original coordinates
of the array.

chunk-offset compression

One common MOLAP approach stores data in
chunked multidimensional arrays. Indices into
an array are obtained by a normalization process
that maps attribute values to integers.
In this scheme the large multidimensional arrays
are broken into chunks for storage and process-
ing (Sarawagi & Stonebraker 1994). Consider
some normalized n-dimensional array A, whose
dimensionality is dd

compressed row/ column Storage
for Multidimensional Arrays

Compressed Row Storage (CRS) and Compressed
Column Storage (CCS) (Barret et, al; 1994 and
White & Sadayappan, 1997) are commonly used
due to their simplicity and purity with a weak
dependence relationship between array elements
in a sparse array.
The CRS scheme uses one one-dimensional
floating point array VL and two one-dimensional
integer arrays RO and CO to compress all the
nonzero elements along the rows (columns for
CCS) of the multidimensional sparse array. The

... . The chunks
can be formed by breaking each d i into several
ranges. Within A, two positions are in the same
chunk iff, in every dimension, they fall within the
same range. In memory or disk, values within a
chunk are stored consecutively. Figure 2 shows
a 3 dimensional array divided into sixty chunks
(4×5×3) that are numbered in row-major fashion.

´´´

d n

1