An O(nm) time algorithm for finding the min length directed cycle in a graph

  title={An O(nm) time algorithm for finding the min length directed cycle in a graph},
  author={James B. Orlin and Antonio Sede{\~n}o-Noda},
  booktitle={ACM-SIAM Symposium on Discrete Algorithms},
In this paper, we introduce an O(nm) time algorithm to determine the minimum length directed cycle (also called the "minimum weight directed cycle") in a directed network with n nodes and m arcs and with no negative length directed cycles. This result improves upon the previous best time bound of O(nm + n2 log log n). Our algorithm first determines the cycle with minimum mean length λ* in O(nm) time. Subsequently, it chooses node potentials so that all reduced costs are λ* or greater. It then… 

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