A safe and complete algorithm for metagenomic assembly

Background Reconstructing the genome of a species from short fragments is one of the oldest bioinformatics problems. Metagenomic assembly is a variant of the problem asking to reconstruct the circular genomes of all bacterial species present in a sequencing sample. This problem can be naturally formulated as finding a collection of circular walks of a directed graph G that together cover all nodes, or edges, of G . Approach We address this problem with the “safe and complete” framework of Tomescu and Medvedev (Research in computational Molecular biology—20th annual conference, RECOMB 9649:152–163, 2016 ). An algorithm is called safe if it returns only those walks (also called safe ) that appear as subwalk in all metagenomic assembly solutions for G . A safe algorithm is called complete if it returns all safe walks of G . Results We give graph-theoretic characterizations of the safe walks of G , and a safe and complete algorithm finding all safe walks of G . In the node-covering case, our algorithm runs in time O(m^2 + n^3) , and in the edge-covering case it runs in time O(m^2n) ; n and m denote the number of nodes and edges, respectively, of G . This algorithm constitutes the first theoretical tight upper bound on what can be safely assembled from metagenomic reads using this problem formulation.