Figure 1.

Example of the layout optimization. The figure on the left side shows an explicit phylogenetic network. The reticulation edges of the network are shown as dashed lines. Removing the reticulation edges and integrating the auxiliary edges into the network leads to a tree structure, as shown on the right-hand side of the figure (auxiliary edges are drawn as dashed lines). The set of easily reachable edges R_v of the node v contains the reticulations r1, r2, r3, r4 and r*. The set only contains r* and is equal to . The placement of r* has cost 1 since the reticulation edges only cross the edge that leads to leaf g. The placement of r4 has cost 2, since the reticulation edges to the right crosses r1 and r3.