Finding a long directed cycle

Authors:
Harold N. Gabow;Shuxin Nie
Affiliations:
University of Colorado at Boulder, Boulder, Colorado;University of Colorado at Boulder, Boulder, Colorado
Venue:
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2004

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Abstract

For fixed k we present linear and almost-linear time algorithms to find a directed cycle of length ≥ k, if one exists. We find a directed cycle of length ≥ log n/log log n in polynomial time, if one exists. Under an appropriate complexity assumption it is known to be impossible to improve this by more than a log log n factor. Our approach is based on depth-first search.