Minimizing number of crossings in a bipartite graph
问题 The following algorithm problem occurred to me while drawing a graph for something unrelated: We have a plane drawing of a bipartite graph, with the disjoint sets arranged in columns as shown. How can we rearrange the nodes within each column so that the number of edge crossings is minimized? I know this problem is NP-hard for general graphs (link), but is there some trick considering that the graph is bipartite? As a follow-up, what if there is a third column w , which only has edges to v ?