Efficient construction of an assembly string graph using the FM-index

Abstract

Motivation: Sequence assembly is a difficult problem whose importance has grown again recently as the cost of sequencing has dramatically dropped. Most new sequence assembly software has started by building a de Bruijn graph, avoiding the overlap-based methods used previously because of the computational cost and complexity of these with very large numbers of short reads. Here, we show how to use suffix array-based methods that have formed the basis of recent very fast sequence mapping algorithms to find overlaps and generate assembly string graphs asymptotically faster than previously described algorithms.

Results: Standard overlap assembly methods have time complexity O(N(2)), where N is the sum of the lengths of the reads. We use the Ferragina-Manzini index (FM-index) derived from the Burrows-Wheeler transform to find overlaps of length at least tau among a set of reads. As well as an approach that finds all overlaps then implements transitive reduction to produce a string graph, we show how to output directly only the irreducible overlaps, significantly shrinking memory requirements and reducing compute time to O(N), independent of depth. Overlap-based assembly methods naturally handle mixed length read sets, including capillary reads or long reads promised by the third generation sequencing technologies. The algorithms we present here pave the way for overlap-based assembly approaches to be developed that scale to whole vertebrate genome de novo assembly.

Fig. 1.

Diagram of a simple string graph. Three overlapping reads (R₁, R₂, R₃) are shown in (A). (B) shows the string graph constructed from the overlaps between the reads. The arrowheads pointing into the nodes depict an edge of type B and arrowheads pointing away from the nodes depict edges of type E. The edge R₁ ↔ R₃ is transitive.

Fig. 2.

The running time of the direct and exhaustive overlap algorithms for simulated E. coli data with sequence depth from 5× to 100×. The direct overlap algorithm scales linearly with sequence depth. As the number of overlaps grows quadratically with sequence depth, the exhaustive overlap algorithm exhibits above-linear scaling.