Fig. 2

Minimum feedback arc set (MFAS) does not necessarily yield an optimial solution of the SSP. Due to the arbitrariness of the orientation of the edges, the best solution of the SSP may contain cycles, which by definition is excluded in MFAS. Top: supergenome graph representation \(\Gamma (\mathfrak{A})\) of an artificial alignment \(\mathfrak{A}\). Bottom: simplified solution of the (uniformly weighted) MFAS. To turn \(\Gamma (\mathfrak{A})\) into an acyclic graph, at least one edge has to be deleted. Two such solutions exist, differing only by the orientation of the gray arrow. The corresponding topological sorting breaks the genome into two distinct colinear pieces with opposite orientation. There is, however, a consistent order of the entire graph—the linear left-to-right or right-to-left order is consistent