A safe and complete algorithm for metagenomic assembly

Abstract

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(m2 + n3), and in the edge-covering case it runs in time O(m2n); 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.