FIG. 1.

(A) An example of a de Bruijn graph for a set K with 9 3-mers. The 0 side of a vertex is drawn flat and the 1 side pointy. The text in each vertex is its label, that is, what is spelled by a walk going in the direction of the pointy end. The string below the vertex is the reverse complement of its label, which is what is spelled by a walk going in the opposite direction. The maximal unitigs are shown by filled in gray arrows. (B) The compacted de Bruijn graph for the same set K. Each vertex corresponds to a maximal unitig in the top graph. Each vertex's label corresponds to the spelling of the corresponding unitig and is shown inside the vertex; the reverse complement of the label is written below in italics. One possible path cover is five walks, each corresponding to a single vertex; the spelling of this cover is $\left\{AAAC,ACGG,ACTGG,GGA,ACC\right\}$, which is the unitig SPSS representation of K. A better path cover of size 2 that could potentially be found by our UST algorithm is shown. It corresponds to SPSS representation $\left\{AAACGGA,ACTGGT\right\}$. It is easy to verify that this path cover has minimum size, and, by Theorem 1, the corresponding representation has minimum weight (13). (C) Another path cover that could potentially be found by UST. It has size 3 and is suboptimal. SPSS, spectrum-preserving string set; UST, Unitig-STitch.