Compressed weighted de Bruijn graphs

We propose a new compressed representation for weighted de Bruijn graphs, which is based on the idea of delta-encoding the variations of k-mer abundances on a spanning branching of the graph. Our new data structure is likely to be of practical value: to give an idea, when combined with the compressed BOSS de Bruijn graph representation, it encodes the weighted de Bruijn graph of a 16x-covered DNA read-set (60M distinct k-mers, k = 28) within 4.15 bits per distinct k-mer and can answer abundance queries in about 60 microseconds on a standard machine. In contrast, state of the art tools declare a space usage of at least 30 bits per distinct k-mer for the same task, which is confirmed by our experiments. As a by-product of our new data structure, we exhibit efficient compressed data structures for answering partial sums on edge-weighted trees, which might be of independent interest

Space efficient merging of de Bruijn graphs and Wheeler graphs

The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de Bruijn graphs. Our algorithm has the same asymptotic cost of the state of the art algorithm for the same problem but it uses less than half of its working space. A novel important feature of our algorithm, not found in any of the existing tools, is that it can compute the Variable Order succinct representation of the union graph within the same asymptotic time/space bounds. In the second part of the paper we consider the more general problem of merging succinct representations of Wheeler graphs, a recently introduced graph family which includes as special cases de Bruijn graphs and many other known succinct indexes based on the BWT or one of its variants. We show that Wheeler graphs merging is in general a much more difficult problem, and we provide a space efficient algorithm for the slightly simplified problem of determining whether the union graph has an ordering that satisfies the Wheeler conditions.Comment: 24 pages, 10 figures. arXiv admin note: text overlap with arXiv:1902.0288

Wavelet analysis on symbolic sequences and two-fold de Bruijn sequences

The concept of symbolic sequences play important role in study of complex systems. In the work we are interested in ultrametric structure of the set of cyclic sequences naturally arising in theory of dynamical systems. Aimed at construction of analytic and numerical methods for investigation of clusters we introduce operator language on the space of symbolic sequences and propose an approach based on wavelet analysis for study of the cluster hierarchy. The analytic power of the approach is demonstrated by derivation of a formula for counting of {\it two-fold de Bruijn sequences}, the extension of the notion of de Bruijn sequences. Possible advantages of the developed description is also discussed in context of applied

Using cascading Bloom filters to improve the memory usage for de Brujin graphs

De Brujin graphs are widely used in bioinformatics for processing next-generation sequencing data. Due to a very large size of NGS datasets, it is essential to represent de Bruijn graphs compactly, and several approaches to this problem have been proposed recently. In this work, we show how to reduce the memory required by the algorithm of [3] that represents de Brujin graphs using Bloom filters. Our method requires 30% to 40% less memory with respect to the method of [3], with insignificant impact to construction time. At the same time, our experiments showed a better query time compared to [3]. This is, to our knowledge, the best practical representation for de Bruijn graphs.Comment: 12 pages, submitte

Relative Select

Motivated by the problem of storing coloured de Bruijn graphs, we show how, if we can already support fast select queries on one string, then we can store a little extra information and support fairly fast select queries on a similar string

Efficient tilings of de Bruijn and Kautz graphs

Kautz and de Bruijn graphs have a high degree of connectivity which makes them ideal candidates for massively parallel computer network topologies. In order to realize a practical computer architecture based on these graphs, it is useful to have a means of constructing a large-scale system from smaller, simpler modules. In this paper we consider the mathematical problem of uniformly tiling a de Bruijn or Kautz graph. This can be viewed as a generalization of the graph bisection problem. We focus on the problem of graph tilings by a set of identical subgraphs. Tiles should contain a maximal number of internal edges so as to minimize the number of edges connecting distinct tiles. We find necessary and sufficient conditions for the construction of tilings. We derive a simple lower bound on the number of edges which must leave each tile, and construct a class of tilings whose number of edges leaving each tile agrees asymptotically in form with the lower bound to within a constant factor. These tilings make possible the construction of large-scale computing systems based on de Bruijn and Kautz graph topologies.Comment: 29 pages, 11 figure