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We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…

Data Structures and Algorithms · Computer Science 2021-09-06 J. Ian Munro , Patrick K. Nicholson , Louisa Seelbach Benkner , Sebastian Wild

The Burrows-Wheeler transform (BWT) is a string transformation that enhances string indexing and compressibility. Cotumaccio and Prezza [SODA '21] extended this transformation to nondeterministic finite automata (NFAs) through…

Data Structures and Algorithms · Computer Science 2025-03-11 Ruben Becker , Nicola Cotumaccio , Sung-Hwan Kim , Nicola Prezza , Carlo Tosoni

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)…

Databases · Computer Science 2016-08-02 Daniel Lemire , Owen Kaser , Kamel Aouiche

Indexing very large collections of strings, such as those produced by the widespread next generation sequencing technologies, heavily relies on multistring generalization of the Burrows-Wheeler Transform (BWT): large requirements of…

Data Structures and Algorithms · Computer Science 2020-12-07 Paola Bonizzoni , Gianluca Della Vedova , Yuri Pirola , Marco Previtali , Raffaella Rizzi

Summary: We present a new method to incrementally construct the FM-index for both short and long sequence reads, up to the size of a genome. It is the first algorithm that can build the index while implicitly sorting the sequences in the…

Genomics · Quantitative Biology 2014-08-29 Heng Li

DNA sequencing technology has advanced to a point where storage is becoming the central bottleneck in the acquisition and mining of more data. Large amounts of data are vital for genomics research, and generic compression tools, while…

Information Theory · Computer Science 2016-11-15 Bobbie Chern , Idoia Ochoa , Alexandros Manolakos , Albert No , Kartik Venkat , Tsachy Weissman

Mantaci et al. [TCS 2007] defined the eBWT to extend the definition of the BWT to a collection of strings, however, since this introduction, it has been used more generally to describe any BWT of a collection of strings and the fundamental…

Data Structures and Algorithms · Computer Science 2021-06-22 Christina Boucher , Davide Cenzato , Zsuzsanna Lipták , Massimiliano Rossi , Marinella Sciortino

A parameterized string (p-string) is a string over an alphabet $(\Sigma_{s} \cup \Sigma_{p})$, where $\Sigma_{s}$ and $\Sigma_{p}$ are disjoint alphabets for static symbols (s-symbols) and for parameter symbols (p-symbols), respectively.…

Data Structures and Algorithms · Computer Science 2023-08-14 Kento Iseri , Tomohiro I , Diptarama Hendrian , Dominik Köppl , Ryo Yoshinaka , Ayumi Shinohara

Parameterized strings are a generalization of strings in that their characters are drawn from two different alphabets, where one is considered to be the alphabet of static characters and the other to be the alphabet of parameter characters.…

Data Structures and Algorithms · Computer Science 2022-09-01 Daiki Hashimoto , Diptarama Hendrian , Dominik Köppl , Ryo Yoshinaka , Ayumi Shinohara

Text datasets can be represented using models that do not preserve text structure, or using models that preserve text structure. Our hypothesis is that depending on the dataset nature, there can be advantages using a model that preserves…

Information Theory · Computer Science 2025-02-04 Ana Granados , Kostadin Koroutchev , Francisco de Borja Rodríguez

The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several…

Data Structures and Algorithms · Computer Science 2016-05-16 Anthony J. Cox , Fabio Garofalo , Giovanna Rosone , Marinella Sciortino

In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…

Methodology · Statistics 2008-07-25 Ann B. Lee , Boaz Nadler , Larry Wasserman

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)…

Databases · Computer Science 2009-01-19 Owen Kaser , Daniel Lemire , Kamel Aouiche

Relative compression, where a set of similar strings are compressed with respect to a reference string, is a very effective method of compressing DNA datasets containing multiple similar sequences. Relative compression is fast to perform…

Quantitative Methods · Quantitative Biology 2011-06-21 Shanika Kuruppu , Simon Puglisi , Justin Zobel

Summary: Longer sequencing reads, with at least 200 bases per template are now common. While traditional aligners have adopted new strategies to improve the mapping of longer reads, aligners specific to bisulfite-sequencing were optimized…

Genomics · Quantitative Biology 2014-05-14 Brent S. Pedersen , Kenneth Eyring , Subhajyoti De , Ivana V. Yang , David A. Schwartz

Text retrieval using learned sparse representations of queries and documents has, over the years, evolved into a highly effective approach to search. It is thanks to recent advances in approximate nearest neighbor search-with the emergence…

Information Retrieval · Computer Science 2026-02-06 Sebastian Bruch , Martino Fontana , Franco Maria Nardini , Cosimo Rulli , Rossano Venturini

Genome assembly using high throughput data with short reads, arguably, remains an unresolvable task in repetitive genomes, since when the length of a repeat exceeds the read length, it becomes difficult to unambiguously connect the flanking…

Quantitative Methods · Quantitative Biology 2013-07-31 Viraj Deshpande , Eric DK Fung , Son Pham , Vineet Bafna

A labeled tree (or a trie) is a natural generalization of a string, which can also be seen as a compact representation of a set of strings. This paper considers the labeled tree indexing problem, and provides a number of new results on…

Data Structures and Algorithms · Computer Science 2022-01-04 Shunsuke Inenaga

We show that the compressed suffix array and the compressed suffix tree for a string of length $n$ over an integer alphabet of size $\sigma\leq n$ can both be built in $O(n)$ (randomized) time using only $O(n\log\sigma)$ bits of working…

Data Structures and Algorithms · Computer Science 2016-05-24 Djamal Belazzougui

Advances in DNA sequencing technology will soon result in databases of thousands of genomes. Within a species, individuals' genomes are almost exact copies of each other; e.g., any two human genomes are 99.9% the same. Relative Lempel-Ziv…

Data Structures and Algorithms · Computer Science 2011-11-08 Travis Gagie , Juha Kärkkäinen , Yakov Nekrich , Simon J. Puglisi
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