FIG. 4.

Illustration of bulge removal algorithms. For illustrative purposes, the vertices of the condensed graph are shown in white; the additional vertices present in the uncondensed graph are shown as small solid circles in the color (black, red, or blue) of the condensed edge on which they lie. Dotted green arrows indicate projection operations (not graph edges). (a–c) Algorithm A: The bulge corremoval algorithm from Bankevich et al. (2012). (a) A bulge in the de Bruijn graph. In (b), the blue edges have alternative paths while the red edges do not have alternative paths. After applying the bulge corremoval procedure to the blue edges, graph (b) is transformed into graph (c). There are now alternative paths for red edges in (c), and the graph is further transformed into a single condensed edge representing the bold path in (c). (e–f) Algorithm B: Merging paths instead of projecting paths. Merging two paths in (e) results in a graph (f) with an artificial (blue) path violating condition (ii). (g–h) Algorithm C: Blob corremoval. Complex bulge (g) is not removed by the bulge corremoval procedure from Bankevich et al. (2012). Applying the new “blob corremoval procedure” to blob (g) simplifies it via the projections shown in (h). Thick edges denote the tree to which we project the blob. The blob corremoval procedure may also be applied to (a) to directly simplify it to a single condensed edge in one step via the projections shown in (d); this achieves the same result as bulge corremoval did with two sets of projections, (b) and (c).