Nonconstructive tools for proving polynomial-time decidability
Journal of the ACM (JACM)
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On linear time minor tests with depth-first search
Journal of Algorithms
Regular Article: On search, decision, and the efficiency of polynomial-time algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
Journal of the ACM (JACM)
Approximating the Minimum Equivalent Digraph
SIAM Journal on Computing
Finding Even Cycles Even Faster
SIAM Journal on Discrete Mathematics
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Finding a Path of Superlogarithmic Length
SIAM Journal on Computing
Finding Paths and Cycles of Superpolylogarithmic Length
SIAM Journal on Computing
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Consider a digraph with n vertices. For any fixed value k, we present linear- and almost-linear-time algorithms to find a cycle of length ≥ k, if one exists. We also find a cycle that has 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 guarantee by more than a log log n factor. Our approach is based on depth-first search.