Compressing High-Dimensional Data Spaces Using Non-Differential Augmented Vector Quantization

query processing times and space requirements. Database compression has been discovered to alleviate the I/O bottleneck, reduce disk space, improve disk access speed, speed up query, reduce overall retrieval time and increase the effective I/O bandwidth. However, random access to individual tuples in a compressed database is very difficult to achieve with most available compression techniques. We propose a lossless compression technique called non-differential augmented vector quantization, a close variant of the novel augmented vector quantization. The technique is applicable to a collection of tuples and especially effective for tuples with many low to medium cardinality fields. In addition, the technique supports standard database operations, permits very fast random access and atomic decompression of tuples in large collections. The technique maps a database relation into a static bitmap index cached access structure. Consequently, we were able to achieve substantial savings in space by storing each database tuple as a bit value in the computer memory. Important distinguishing characteristics of our technique is that individual tuples can be compressed and decompressed, rather than a full page or entire relation at a time, (b) the information needed for tuple compression and decompression can reside in the memory or at worst in a single page. Promising application domains include decision support systems, statistical databases and life databases with low cardinality fields and possibly no text field

Attribute Value Reordering For Efficient Hybrid OLAP

The normalization of a data cube is the ordering of the attribute values. For large multidimensional arrays where dense and sparse chunks are stored differently, proper normalization can lead to improved storage efficiency. We show that it is NP-hard to compute an optimal normalization even for 1x3 chunks, although we find an exact algorithm for 1x2 chunks. When dimensions are nearly statistically independent, we show that dimension-wise attribute frequency sorting is an optimal normalization and takes time O(d n log(n)) for data cubes of size n^d. When dimensions are not independent, we propose and evaluate several heuristics. The hybrid OLAP (HOLAP) storage mechanism is already 19%-30% more efficient than ROLAP, but normalization can improve it further by 9%-13% for a total gain of 29%-44% over ROLAP

Histogram-Aware Sorting for Enhanced Word-Aligned Compression in Bitmap Indexes

Bitmap indexes must be compressed to reduce input/output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH) compression. These techniques are sensitive to the order of the rows: a simple lexicographical sort can divide the index size by 9 and make indexes several times faster. We investigate reordering heuristics based on computed attribute-value histograms. Simply permuting the columns of the table based on these histograms can increase the sorting efficiency by 40%.Comment: To appear in proceedings of DOLAP 200

Attribute Value Reordering for Efficient Hybrid OLAP

The normalization of a data cube is the process of choosing an ordering for the attribute values, and the chosen ordering will affect the physical storage of the cube's data. For large multidimensional arrays, proper normalization can lead to more efficient storage in hybrid OLAP contexts that store dense and sparse chunks differently. We show that it is NP-hard to compute an optimal normalization even for 1x3 chunks, although we find an exact algorithm for 1x2 chunks. When attributes are nearly statistically independent, we show that an optimal normalization is given by dimension-wise attribute frequency sorting, which can be done in time O(d n log(n)) for data cubes of size n^d. When attributes are not independent, we propose and evaluate a number of heuristics.\ud \ud Our optimized hybrid OLAP storage mechanism was observed to be 44% more storage efficient than ROLAP and the gains due to normalization alone accounted for 45% of this increase in efficiency

Universal Indexes for Highly Repetitive Document Collections

Indexing highly repetitive collections has become a relevant problem with the emergence of large repositories of versioned documents, among other applications. These collections may reach huge sizes, but are formed mostly of documents that are near-copies of others. Traditional techniques for indexing these collections fail to properly exploit their regularities in order to reduce space. We introduce new techniques for compressing inverted indexes that exploit this near-copy regularity. They are based on run-length, Lempel-Ziv, or grammar compression of the differential inverted lists, instead of the usual practice of gap-encoding them. We show that, in this highly repetitive setting, our compression methods significantly reduce the space obtained with classical techniques, at the price of moderate slowdowns. Moreover, our best methods are universal, that is, they do not need to know the versioning structure of the collection, nor that a clear versioning structure even exists. We also introduce compressed self-indexes in the comparison. These are designed for general strings (not only natural language texts) and represent the text collection plus the index structure (not an inverted index) in integrated form. We show that these techniques can compress much further, using a small fraction of the space required by our new inverted indexes. Yet, they are orders of magnitude slower.Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 69094

Lossless Astronomical Image Compression and the Effects of Noise

We compare a variety of lossless image compression methods on a large sample of astronomical images and show how the compression ratios and speeds of the algorithms are affected by the amount of noise in the images. In the ideal case where the image pixel values have a random Gaussian distribution, the equivalent number of uncompressible noise bits per pixel is given by Nbits =log2(sigma * sqrt(12)) and the lossless compression ratio is given by R = BITPIX / Nbits + K where BITPIX is the bit length of the pixel values and K is a measure of the efficiency of the compression algorithm. We perform image compression tests on a large sample of integer astronomical CCD images using the GZIP compression program and using a newer FITS tiled-image compression method that currently supports 4 compression algorithms: Rice, Hcompress, PLIO, and GZIP. Overall, the Rice compression algorithm strikes the best balance of compression and computational efficiency; it is 2--3 times faster and produces about 1.4 times greater compression than GZIP. The Rice algorithm produces 75%--90% (depending on the amount of noise in the image) as much compression as an ideal algorithm with K = 0. The image compression and uncompression utility programs used in this study (called fpack and funpack) are publicly available from the HEASARC web site. A simple command-line interface may be used to compress or uncompress any FITS image file.Comment: 20 pages, 9 figures, to be published in PAS