I ran across this problem a while ago, working on identifying edges in
dependence cycles for software pipelining. The problem you want to solve is
known as the "minimum feedback arc set" problem and is NP-hard. In my case,
I could use other knowledge about the problem domain to find a good
approximate solution.
I'll refer you to the Wikipedia article:
http://en.wikipedia.org/wiki/Feedback_arc_set
I hope that helps.
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