Manifold de Bruijn Graphs

Genome assembly is usually abstracted as the problem of reconstructing a string from a set of its k-mers. This abstraction naturally leads to the classical de Bruijn graph approach-the key algorithmic technique in genome assembly. While each vertex in this approach is labeled by a string of the fixed length k, the recent genome assembly studies suggest that it would be useful to generalize the notion of the de Bruijn graph to the case when vertices are labeled by strings of variable lengths. Ideally, we would like to choose larger values of k in high-coverage regions to reduce repeat collapsing and smaller values of k in the low-coverage regions to avoid fragmentation of the de Bruijn graph. To address this challenge, the iterative de Bruijn graph assembly (IDBA) approach allows one to increase k at each iterations of the graph construction. We introduce the Manifold de Bruijn (M-Bruijn) graph (that generalizes the concept of the de Bruijn graph) and show that it can provide benefits similar to the IDBA approach in a single iteration that considers the entire range of possible k-mer sizes rather than varies k from one iteration to another.