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- ItemA framework for space-efficient read clustering in metagenomic samples(BioMed Central, 2017-03-14) Alanko, Jarno; Cunial, Fabio; Belazzougui, Djamal; Mäkinen, Veli
Show more Background: A metagenomic sample is a set of DNA fragments, randomly extracted from multiple cells in an environment, belonging to distinct, often unknown species. Unsupervised metagenomic clustering aims at partitioning a metagenomic sample into sets that approximate taxonomic units, without using reference genomes. Since samples are large and steadily growing, space-efficient clustering algorithms are strongly needed. Results: We design and implement a space-efficient algorithmic framework that solves a number of core primitives in unsupervised metagenomic clustering using just the bidirectional Burrows-Wheeler index and a union-find data structure on the set of reads. When run on a sample of total length n, with m reads of maximum length ℓ each, on an alphabet of total size σ, our algorithms take O(n(t+logσ)) time and just 2n+o(n)+O(max{ℓ σlogn,K logm}) bits of space in addition to the index and to the union-find data structure, where K is a measure of the redundancy of the sample and t is the query time of the union-find data structure. Conclusions: Our experimental results show that our algorithms are practical, they can exploit multiple cores by a parallel traversal of the suffix-link tree, and they are competitive both in space and in time with the state of the art.Show more - ItemBidirectional Variable-Order de Bruijn Graphs(Springer International Publishing, 2016-03-22) Belazzougui, Djamal; Gagie, Travis; Mäkinen, Veli; Previtali, Marco; Puglisi, Simon J.
Show more Implementing de Bruijn graphs compactly is an important problem because of their role in genome assembly. There are currently two main approaches, one using Bloom filters and the other using a kind of Burrows-Wheeler Transform on the edge labels of the graph. The second representation is more elegant and can even handle many graph-orders at once, but it does not cleanly support traversing edges backwards or inserting new nodes or edges. In this paper we resolve the first of these issues and partially address the second.Show more - ItemBidirectional Variable-Order de Bruijn Graphs(World Scientific Publishing, 2018-12) Belazzougui, Djamal; Gagie, Travis; Mäkinen, Veli; Previtali, Marco; Puglisi, Simon J.
Show more Compressed suffix trees and bidirectional FM-indexes can store a set of strings and support queries that let us explore the set of substrings they contain, adding and deleting characters on both the left and right, but they can use much more space than a de Bruijn graph for the strings. Bowe et al.’s BWT-based de Bruijn graph representation (Proc. Workshop on Algorithms for Bioinformatics, pp. 225–235, 2012) can be made bidirectional as well, at the cost of increasing its space usage by a small constant, but it fixes the length of the substrings. Boucher et al. (Proc. Data Compression Conference, pp. 383–392, 2015) generalized Bowe et al.’s representation to support queries about variable-length substrings, but at the cost of bidirectionality. In this paper we show how to make Boucher et al.’s variable-order implementation of de Bruijn graphs bidirectional.Show more - ItemFully Dynamic de Bruijn Graphs(Springer International Publishing, 2016-09-21) Belazzougui, Djamal; Gagie, Travis; Mäkinen, Veli; Previtali, Marco
Show more We present a space- and time-efficient fully dynamic implementation of de Bruijn graphs, which can also support fixed-length jumbled pattern matching.Show more - ItemLinear-time string indexing and analysis in small space(Association for Computing Machinery, 2020-03-09) Belazzougui, Djamal; Cunial, Fabio; Kärkkäinen, Juha; Mäkinen, Veli
Show more The field of succinct data structures has flourished over the last 16 years. Starting from the compressed suffix array by Grossi and Vitter (STOC 2000) and the FM-index by Ferragina and Manzini (FOCS 2000), a number of generalizations and applications of string indexes based on the Burrows-Wheeler transform (BWT) have been developed, all taking an amount of space that is close to the input size in bits. In many large-scale applications, the construction of the index and its usage need to be considered as one unit of computation. For example, one can compare two genomes by building a common index for their concatenation, and by detecting common substructures by querying the index. Efficient string indexing and analysis in small space lies also at the core of a number of primitives in the data-intensive field of high-throughput DNA sequencing. We report the following advances in string indexing and analysis. We show that the BWT of a string T ∈ {1, . . . ,σ }^n can be built in deterministic O (n) time using just O (n log σ ) bits of space, where σ ≤ n. Deterministic linear time is achieved by exploiting a new partial rank data structure that supports queries in constant time, and that might have independent interest. Within the same time and space budget, we can build an index based on the BWT that allows one to enumerate all the internal nodes of the suffix tree of T . Many fundamental string analysis problems, such as maximal repeats, maximal unique matches, and string kernels, can be mapped to such enumeration, and can thus be solved in deterministic O (n) time and in O (n log σ ) bits of space from the input string, by tailoring the enumeration algorithm to some problem-specific computations. We also show how to build many of the existing indexes based on the BWT, such as the compressed suffix array, the compressed suffix tree, and the bidirectional BWT index, in randomized O (n) time and in O (n log σ ) bits of space. The previously fastest construction algorithms for BWT, compressed suffix array and compressed suffix tree, which used O (n log σ ) bits of space, took O (n log log σ ) time for the first two structures, and O (n log^ϵ n) time for the third, where ϵ is any positive constant smaller than one. Alternatively, the BWT could be previously built in linear time if one was willing to spend O (n log σ log log_σ n) bits of space. Contrary to the state of the art, our bidirectional BWT index supports every operation in constant time per element in its output.Show more