Choosing an order for constructing a de Bruijn graph (DBG) is a crucial step in de novo assembly, as no single value allows complete genome reconstruction. The variable-order de Bruijn graph (voDBG) addresses this limitation by combining DBGs of multiple orders in a single structure connected by contextual relationships. This representation enables new connections to be identified or ambiguities to be resolved during assembly. However, voDBGs currently lack a formal definition of contigs. In this paper, we give the first formal definition of contigs for voDBGs. We show that, for a frequency range [𝓁,h] with 𝓁 > h/2, nodes whose labels occur with frequency f ∈ [𝓁, h] in the reads spell sequences of the genome with high probability under uniform sampling assumptions. We call these sequences (𝓁,h)-tigs. We also present an efficient algorithm to enumerate (𝓁,h)-tigs from a voDBG that accounts for homopolymer errors. Experiments on PacBio HiFi data show that our method significantly improves contiguity compared to unitigs in fixed-order DBGs while remaining considerably lighter than full genome assemblers.

We present a new semi-external algorithm that builds the Burrows–Wheeler transform variant of Bauer et al. (a.k.a., BCR BWT) in linear expected time. Our method uses compression techniques to reduce computational costs when the input is massive and repetitive. Concretely, we build on induced suffix sorting (ISS) and resort to run-length and grammar compression to maintain our intermediate results in compact form. Our compression format not only saves space but also speeds up the required computations. Our experiments show important space and computation time savings when the text is repetitive. In moderate-size collections of real human genome assemblies (14.2 GB - 75.05 GB), our memory peak is, on average, 1.7x smaller than the peak of the state-of-the-art BCR BWT construction algorithm (ropebwt2), while running 5x faster. Our current implementation was also able to compute the BCR BWT of 400 real human genome assemblies (1.2 TB) in 41.21 hours using 118.83 GB of working memory (around 10% of the input size). Interestingly, the results we report in the 1.2 TB file are dominated by the difficulties of scanning huge files under memory constraints (specifically, I/O operations). This fact indicates we can perform much better with a more careful implementation of our method, thus scaling to even bigger sizes efficiently.

We describe a grammar for DNA sequencing reads from which we can compute the BWT directly. Our motivation is to perform in succinct space genomic analyses that require complex string queries not yet supported by repetition-based self-indexes. Our approach is to store the set of reads as a grammar, but when required, compute its BWT to carry out the analysis by using self-indexes. Our experiments in real data showed that the space reduction we achieve with our compressor is competitive with LZ-based methods and better than entropy-based approaches. Compared to other popular grammars, in this kind of data, we achieve, on average, 12% extra compression and require less working space and time.

Converting a set of sequencing reads into a lossless compact data structure that encodes all the relevant biological information is a major challenge. The classical approaches are to build the string graph or the de Bruijn graph (dBG) of some order k. Each has advantages over the other depending on the application. Still, the ideal setting would be to have an index of the reads that is easy to build and can be adapted to any type of biological analysis. In this paper we propose rBOSS, a new data structure based on the Burrows-Wheeler Transform (BWT), which gets close to that ideal. Our rBOSS simultaneously encodes all the dBGs of a set of sequencing reads up to some order k, and for any dBG node v, it can compute in O(k) time all the other nodes whose labels have an overlap of at least m characters with the label of v, with m being a parameter. If we choose the parameter k equal to the size of the reads (assuming that all have equal length), then we can simulate the overlap graph of the read set. Instead of storing the edges of this graph explicitly, rBOSS computes them on the fly as we traverse the graph. As most BWT-based structures, rBOSS is unidirectional, meaning that we can retrieve only the suffix overlaps of the nodes. However, we exploit the property of the DNA reverse complements to simulate bi-directionality. We implemented a genome assembler on top of rBOSS to demonstrate its usefulness. The experimental results show that, using k=100, our rBOSS-based assembler can process ~500K reads of 150 characters long each (a FASTQ file of 185 MB) in less than 15 minutes and using 110 MB in total. It produces contigs of mean sizes over 10,000, which is twice the size obtained by using a pure de Bruijn graph of fixed length k.