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

Re-Pair Compression of Inverted Lists

Compression of inverted lists with methods that support fast intersection operations is an active research topic. Most compression schemes rely on encoding differences between consecutive positions with techniques that favor small numbers. In this paper we explore a completely different alternative: We use Re-Pair compression of those differences. While Re-Pair by itself offers fast decompression at arbitrary positions in main and secondary memory, we introduce variants that in addition speed up the operations required for inverted list intersection. We compare the resulting data structures with several recent proposals under various list intersection algorithms, to conclude that our Re-Pair variants offer an interesting time/space tradeoff for this problem, yet further improvements are required for it to improve upon the state of the art

CONCISE: Compressed 'n' Composable Integer Set

Bit arrays, or bitmaps, are used to significantly speed up set operations in several areas, such as data warehousing, information retrieval, and data mining, to cite a few. However, bitmaps usually use a large storage space, thus requiring compression. Nevertheless, there is a space-time tradeoff among compression schemes. The Word Aligned Hybrid (WAH) bitmap compression trades some space to allow for bitwise operations without first decompressing bitmaps. WAH has been recognized as the most efficient scheme in terms of computation time. In this paper we present CONCISE (Compressed 'n' Composable Integer Set), a new scheme that enjoys significatively better performances than those of WAH. In particular, when compared to WAH, our algorithm is able to reduce the required memory up to 50%, by having similar or better performance in terms of computation time. Further, we show that CONCISE can be efficiently used to manipulate bitmaps representing sets of integral numbers in lieu of well-known data structures such as arrays, lists, hashtables, and self-balancing binary search trees. Extensive experiments over synthetic data show the effectiveness of our approach.Comment: Preprint submitted to Information Processing Letters, 7 page

Optimizing Frequency Queries for Data Mining Applications

Data mining algorithms use various Trie and bitmap-based representations to optimize the support (i.e., frequency) counting performance. In this paper, we compare the memory requirements and support counting performance of FP Tree, and Compressed Patricia Trie against several novel variants of vertical bit vectors. First, borrowing ideas from the VLDB domain, we compress vertical bit vectors using WAH encoding. Second, we evaluate the Gray code rank-based transaction reordering scheme, and show that in practice, simple lexicographic ordering, obtained by applying LSB Radix sort, outperforms this scheme. Led by these results, we propose HDO, a novel Hamming-distance-based greedy transaction reordering scheme, and aHDO, a linear-time approximation to HDO. We present results of experiments performed on 15 common datasets with varying degrees of sparseness, and show that HDO- reordered, WAH encoded bit vectors can take as little as 5% of the uncompressed space, while aHDO achieves similar compression on sparse datasets. Finally, with results from over a billion database and data mining style frequency query executions, we show that bitmap-based approaches result in up to hundreds of times faster support counting, and HDO-WAH encoded bitmaps offer the best space-time tradeoff