Building Fragment Assembly String Graphs

We present a concept and formalism, the string graph, that represents all that is inferable about a DNA sequence from a collection of shotgun sequencing reads collected from it. We give time and space efficient algorithms for constructing a string graph given t he collection of overlaps between the reads and in particular, present a novel linear expected time algorithm for transitive reduction in this context. The result demonstrates that the decomposition of reads into k-mers employed in the de Bruijn graph approach of Pevzner et al. is not essential and in fact creates both efficiency problems and unecessary conceptual complexities. The current paper is the first in a series and presents the basic algorithm and preliminary results that demonstrate the efficiency and scalability of the method. The result is a step toward a next-generation whole genome shotgun assembler that will easily scale to mammalian genomes.