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1. deBGR: an efficient and near-exact representation of the weighted de Bruijn graph

   https://doi.org/10.1093/bioinformatics/btx261  

   Pandey, Prashant ; Bender, Michael A. ; Johnson, Rob ; Patro, Rob ( July 2017 , Bioinformatics)

   Almost all de novo short-read genome and transcriptome assemblers start by building a representation of the de Bruijn Graph of the reads they are given as input. Even when other approaches are used for subsequent assembly (e.g. when one is using ‘long read’ technologies like those offered by PacBio or Oxford Nanopore), efficient k-mer processing is still crucial for accurate assembly, and state-of-the-art long-read error-correction methods use de Bruijn Graphs. Because of the centrality of de Bruijn Graphs, researchers have proposed numerous methods for representing de Bruijn Graphs compactly. Some of these proposals sacrifice accuracy to save space. Further, none of these methods store abundance information, i.e. the number of times that each k-mer occurs, which is key in transcriptome assemblers.

   We present a method for compactly representing the weighted de Bruijn Graph (i.e. with abundance information) with essentially no errors. Our representation yields zero errors while increasing the space requirements by less than 18–28% compared to the approximate de Bruijn graph representation in Squeakr. Our technique is based on a simple invariant that all weighted de Bruijn Graphs must satisfy, and hence is likely to be of general interest and applicable in most weighted de Bruijn Graph-based systems.

   https://github.com/splatlab/debgr.

   Supplementary data are available at Bioinformatics online.

    

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2. On the Hardness and Inapproximability of Recognizing Wheeler Graphs

   https://doi.org/10.4230/LIPIcs.ESA.2019.51  

   Gibney, Daniel ;  Thankachan, Sharma V. ( January 2019 , 27th Annual European Symposium on Algorithms (ESA) 2019)

   In recent years several compressed indexes based on variants of the Burrows-Wheeler transformation have been introduced. Some of these are used to index structures far more complex than a single string, as was originally done with the FM-index [Ferragina and Manzini, J. ACM 2005]. As such, there has been an increasing effort to better understand under which conditions such an indexing scheme is possible. This has led to the introduction of Wheeler graphs [Gagie et al., Theor. Comput. Sci., 2017]. Gagie et al. showed that de Bruijn graphs, generalized compressed suffix arrays, and several other BWT related structures can be represented as Wheeler graphs and that Wheeler graphs can be indexed in a way which is space-efficient. Hence, being able to recognize whether a given graph is a Wheeler graph, or being able to approximate a given graph by a Wheeler graph, could have numerous applications in indexing. Here we resolve the open question of whether there exists an efficient algorithm for recognizing if a given graph is a Wheeler graph. We present - The problem of recognizing whether a given graph G=(V,E) is a Wheeler graph is NP-complete for any edge label alphabet of size sigma >= 2, even when G is a DAG. This holds even on a restricted, subset of graphs called d-NFA's for d >= 5. This is in contrast to recent results demonstrating the problem can be solved in polynomial time for d-NFA's where d <= 2. We also show the recognition problem can be solved in linear time for sigma =1; - There exists an 2^{e log sigma + O(n + e)} time exact algorithm where n = |V| and e = |E|. This algorithm relies on graph isomorphism being computable in strictly sub-exponential time; - We define an optimization variant of the problem called Wheeler Graph Violation, abbreviated WGV, where the aim is to remove the minimum number of edges in order to obtain a Wheeler graph. We show WGV is APX-hard, even when G is a DAG, implying there exists a constant C >= 1 for which there is no C-approximation algorithm (unless P = NP). Also, conditioned on the Unique Games Conjecture, for all C >= 1, it is NP-hard to find a C-approximation; - We define the Wheeler Subgraph problem, abbreviated WS, where the aim is to find the largest subgraph which is a Wheeler Graph (the dual of the WGV). In contrast to WGV, we prove that the WS problem is in APX for sigma=O(1); The above findings suggest that most problems under this theme are computationally difficult. However, we identify a class of graphs for which the recognition problem is polynomial-time solvable, raising the open question of which parameters determine this problem's difficulty. 

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3. Scalable Genome Assembly through Parallel de Bruijn Graph Construction for Multiple k-mers

   https://doi.org/10.1038/s41598-019-51284-9  

   Mahadik, Kanak ; Wright, Christopher ; Kulkarni, Milind ; Bagchi, Saurabh ; Chaterji, Somali ( October 2019 , Scientific Reports)

   Remarkable advancements in high-throughput gene sequencing technologies have led to an exponential growth in the number of sequenced genomes. However, unavailability of highly parallel and scalablede novoassembly algorithms have hindered biologists attempting to swiftly assemble high-quality complex genomes. Popularde Bruijngraph assemblers, such as IDBA-UD, generate high-quality assemblies by iterating over a set ofk-values used in the construction of de Bruijn graphs (DBG). However, this process ofsequentiallyiterating from small to largek-values slows down the process of assembly. In this paper, we propose ScalaDBG, which metamorphoses this sequential process, building DBGs for each distinctk-value in parallel. We develop an innovative mechanism to “patch” a higherk-valued graph with contigs generated from a lowerk-valued graph. Moreover, ScalaDBG leverages multi-level parallelism, by both scaling up on all cores of a node, and scaling out to multiple nodessimultaneously. We demonstrate that ScalaDBG completes assembling the genome faster than IDBA-UD, but with similar accuracy on a variety of datasets (6.8X faster for one of the most complex genome in our dataset).

    

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4. Cuttlefish: fast, parallel and low-memory compaction of de Bruijn graphs from large-scale genome collections

   https://doi.org/10.1093/bioinformatics/btab309  

   Khan, Jamshed ; Patro, Rob ( July 2021 , Bioinformatics)

   null (Ed.)

   Abstract Motivation The construction of the compacted de Bruijn graph from collections of reference genomes is a task of increasing interest in genomic analyses. These graphs are increasingly used as sequence indices for short- and long-read alignment. Also, as we sequence and assemble a greater diversity of genomes, the colored compacted de Bruijn graph is being used more and more as the basis for efficient methods to perform comparative genomic analyses on these genomes. Therefore, time- and memory-efficient construction of the graph from reference sequences is an important problem. Results We introduce a new algorithm, implemented in the tool Cuttlefish, to construct the (colored) compacted de Bruijn graph from a collection of one or more genome references. Cuttlefish introduces a novel approach of modeling de Bruijn graph vertices as finite-state automata, and constrains these automata’s state-space to enable tracking their transitioning states with very low memory usage. Cuttlefish is also fast and highly parallelizable. Experimental results demonstrate that it scales much better than existing approaches, especially as the number and the scale of the input references grow. On a typical shared-memory machine, Cuttlefish constructed the graph for 100 human genomes in under 9 h, using ∼29 GB of memory. On 11 diverse conifer plant genomes, the compacted graph was constructed by Cuttlefish in under 9 h, using ∼84 GB of memory. The only other tool completing these tasks on the hardware took over 23 h using ∼126 GB of memory, and over 16 h using ∼289 GB of memory, respectively. Availability and implementation Cuttlefish is implemented in C++14, and is available under an open source license at https://github.com/COMBINE-lab/cuttlefish. Supplementary information Supplementary data are available at Bioinformatics online. 

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5. Unbiased pangenome graphs

   https://doi.org/10.1093/bioinformatics/btac743  

   Garrison, Erik ; Guarracino, Andrea ( November 2022 , Bioinformatics)

   Alkan, Can (Ed.)

   Abstract Motivation Pangenome variation graphs model the mutual alignment of collections of DNA sequences. A set of pairwise alignments implies a variation graph, but there are no scalable methods to generate such a graph from these alignments. Existing related approaches depend on a single reference, a specific ordering of genomes or a de Bruijn model based on a fixed k-mer length. A scalable, self-contained method to build pangenome graphs without such limitations would be a key step in pangenome construction and manipulation pipelines. Results We design the seqwish algorithm, which builds a variation graph from a set of sequences and alignments between them. We first transform the alignment set into an implicit interval tree. To build up the variation graph, we query this tree-based representation of the alignments to reduce transitive matches into single DNA segments in a sequence graph. By recording the mapping from input sequence to output graph, we can trace the original paths through this graph, yielding a pangenome variation graph. We present an implementation that operates in external memory, using disk-backed data structures and lock-free parallel methods to drive the core graph induction step. We demonstrate that our method scales to very large graph induction problems by applying it to build pangenome graphs for several species. Availability and implementation seqwish is published as free software under the MIT open source license. Source code and documentation are available at https://github.com/ekg/seqwish. seqwish can be installed via Bioconda https://bioconda.github.io/recipes/seqwish/README.html or GNU Guix https://github.com/ekg/guix-genomics/blob/master/seqwish.scm. 

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