H-minor-free graphs, where H can be drawn in the plane with one
crossing, giving an O(n log n) algorithm (assuming a certain
decomposition of the graph is given as input). This algorithm is part
of a body of work whose goal is near-linear time algorithms to compute
maximum flows and minimum cuts in generalizations of planar graphs,
such as minor free graphs and topological graphs. Currently known
algorithms and open problems in this area will both be surveyed.