"Directed" problems that are easier than their "undirected" variant. I was presenting a lecture on pancake sorting, and mentioned that: 


Sorting by reversals is NP-hard
"signed" sorting by reversals is in P. 


Which got me thinking. There is a sense in which "signed" sorting is "directed" - you can view the sign as a direction (and indeed, this is the motivation from evolutionary biology). But it's an easier problem ! This is unusual because generally (at least on graphs) directed problems are harder (or at least as hard) as their undirected counterparts. 


  Assuming a generous definition of "directed", are there any examples
  of directed problems that are easier than their undirected
  counterparts ?
Counting Eulerian circuits for directed graphs is doable in polynomial time using the BEST theorem, while apparently, the same problem for undirected graphs is #P-complete.