Reordering Rows for Better Compression: Beyond the Lexicographic Order

Sorting database tables before compressing them improves the compression rate. Can we do better than the lexicographical order? For minimizing the number of runs in a run-length encoding compression scheme, the best approaches to row-ordering are derived from traveling salesman heuristics, although there is a significant trade-off between running time and compression. A new heuristic, Multiple Lists, which is a variant on Nearest Neighbor that trades off compression for a major running-time speedup, is a good option for very large tables. However, for some compression schemes, it is more important to generate long runs rather than few runs. For this case, another novel heuristic, Vortex, is promising. We find that we can improve run-length encoding up to a factor of 3 whereas we can improve prefix coding by up to 80%: these gains are on top of the gains due to lexicographically sorting the table. We prove that the new row reordering is optimal (within 10%) at minimizing the runs of identical values within columns, in a few cases.Comment: to appear in ACM TOD

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

Large-scale compression of genomic sequence databases with the Burrows-Wheeler transform

Motivation The Burrows-Wheeler transform (BWT) is the foundation of many algorithms for compression and indexing of text data, but the cost of computing the BWT of very large string collections has prevented these techniques from being widely applied to the large sets of sequences often encountered as the outcome of DNA sequencing experiments. In previous work, we presented a novel algorithm that allows the BWT of human genome scale data to be computed on very moderate hardware, thus enabling us to investigate the BWT as a tool for the compression of such datasets. Results We first used simulated reads to explore the relationship between the level of compression and the error rate, the length of the reads and the level of sampling of the underlying genome and compare choices of second-stage compression algorithm. We demonstrate that compression may be greatly improved by a particular reordering of the sequences in the collection and give a novel `implicit sorting' strategy that enables these benefits to be realised without the overhead of sorting the reads. With these techniques, a 45x coverage of real human genome sequence data compresses losslessly to under 0.5 bits per base, allowing the 135.3Gbp of sequence to fit into only 8.2Gbytes of space (trimming a small proportion of low-quality bases from the reads improves the compression still further). This is more than 4 times smaller than the size achieved by a standard BWT-based compressor (bzip2) on the untrimmed reads, but an important further advantage of our approach is that it facilitates the building of compressed full text indexes such as the FM-index on large-scale DNA sequence collections.Comment: Version here is as submitted to Bioinformatics and is same as the previously archived version. This submission registers the fact that the advanced access version is now available at http://bioinformatics.oxfordjournals.org/content/early/2012/05/02/bioinformatics.bts173.abstract . Bioinformatics should be considered as the original place of publication of this article, please cite accordingl

Universal Compressed Text Indexing

The rise of repetitive datasets has lately generated a lot of interest in compressed self-indexes based on dictionary compression, a rich and heterogeneous family that exploits text repetitions in different ways. For each such compression scheme, several different indexing solutions have been proposed in the last two decades. To date, the fastest indexes for repetitive texts are based on the run-length compressed Burrows-Wheeler transform and on the Compact Directed Acyclic Word Graph. The most space-efficient indexes, on the other hand, are based on the Lempel-Ziv parsing and on grammar compression. Indexes for more universal schemes such as collage systems and macro schemes have not yet been proposed. Very recently, Kempa and Prezza [STOC 2018] showed that all dictionary compressors can be interpreted as approximation algorithms for the smallest string attractor, that is, a set of text positions capturing all distinct substrings. Starting from this observation, in this paper we develop the first universal compressed self-index, that is, the first indexing data structure based on string attractors, which can therefore be built on top of any dictionary-compressed text representation. Let $\gamma$ be the size of a string attractor for a text of length $n$. Our index takes $O(\gamma\log(n/\gamma))$ words of space and supports locating the $occ$ occurrences of any pattern of length $m$ in $O(m\log n + occ\log^{\epsilon}n)$ time, for any constant $\epsilon>0$. This is, in particular, the first index for general macro schemes and collage systems. Our result shows that the relation between indexing and compression is much deeper than what was previously thought: the simple property standing at the core of all dictionary compressors is sufficient to support fast indexed queries.Comment: Fixed with reviewer's comment