SIMD Compression and the Intersection of Sorted Integers
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Sorted lists of integers are commonly used in inverted indexes and database systems. They are often compressed in memory. We can use the SIMD instructions available in common processors to boost the speed of integer compression schemes. Our S4-BP128-D4 scheme uses as little as 0.7 CPU cycles per decoded integer while still providing state-of-the-art compression. However, if the subsequent processing of the integers is slow, the effort spent on optimizing decoding speed can be wasted. To show that it does not have to be so, we (1) vectorize and optimize the intersection of posting lists; (2) introduce the SIMD Galloping algorithm. We exploit the fact that one SIMD instruction can compare 4 pairs of integers at once. We experiment with two TREC text collections, GOV2 and ClueWeb09 (Category B), using logs from the TREC million-query track. We show that using only the SIMD instructions ubiquitous in all modern CPUs, our techniques for conjunctive queries can double the speed of a state-of-the-art approach.
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Recent research results in optimizing column-oriented indexes for faster data warehousing. This talks aims to answer the following question: when is sorting the table a sufficiently good optimization?
Compressing column-oriented indexes
Column-oriented databases have become fashionable following the work of Stonebraker et al. In the data warehousing industry, the terms "column oriented" and "column store" have become necessary marketing buzzwords. One of the benefits of column-oriented indexes is good compression through run-length encoding (RLE). This type of compression is particularly benefitial since it simultaneously reduce the volume of data and the necessary computations. However, the efficiency of the compression depends on the order of the rows in the table and this is even more important with larger tables. Finding the best row ordering is NP hard. We compare some heuristics for this problem including variations on the lexicographical order, Gray codes, and Hilbert space-filling curves.
All About Bitmap Indexes... And Sorting Them
A review of bitmap index from an academic perspective. Several theoretical results are presented. The talk also discuss technical issues regarding sorting the tables prior to indexing, as a way to improve the indexes.
Much of the talk is based on the following preprint:
Daniel Lemire, Owen Kaser, Kamel Aouiche, Sorting improves word-aligned bitmap indexes.
http://arxiv.org/abs/0901.3751
A Comparison of Five Probabilistic View-Size Estimation Techniques in OLAP
A data warehouse cannot materialize all possible views, hence we must estimate quickly, accurately, and reliably the size of views to determine the best candidates for materialization. Many available techniques for view-size estimation make particular statistical assumptions and their error can be large. Comparatively, unassuming probabilistic techniques are slower, but they estimate accurately and reliability very large view sizes using little memory. We compare five unassuming hashing-based view-size estimation techniques including Stochastic Probabilistic Counting and LogLog Probabilistic Counting. Our experiments show that only Generalized Counting, Gibbons-Tirthapura, and Adaptive Counting provide universally tight estimates irrespective of the size of the view; of those, only Adaptive Counting remains constantly fast as we increase the memory budget.
Tag-Cloud Drawing: Algorithms for Cloud Visualization
Tag clouds provide an aggregate of tag-usage statistics. They are typically sent as in-line HTML to browsers. However, display mechanisms suited for ordinary text are not ideal for tags, because font sizes may vary widely on a line. As well, the typical layout does not account for relationships that may be known between tags. This paper presents models and algorithms to improve the display of tag clouds that con- sist of in-line HTML, as well as algorithms that use nested tables to achieve a more general 2-dimensional layout in which tag relationships are considered. The first algorithms leverage prior work in typesetting and rectangle packing, whereas the second group of algorithms leverage prior work in Electronic Design Automation. Experiments show our algorithms can be efficiently implemented and perform well.
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%.
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