An Almost Linear Time Approximation Algorithm for the Permanen of a Random (0-1) Matrix

@inproceedings{Frer2004AnAL,
  title={An Almost Linear Time Approximation Algorithm for the Permanen of a Random (0-1) Matrix},
  author={Martin F{\"u}rer and S. Kasiviswanathan},
  booktitle={FSTTCS},
  year={2004}
}
We present a simple randomized algorithm for approximating permanents. The algorithm with inputs A, ∈ > 0 produces an output X A with (1-∈)per(A) 0, and almost all (0-1) matrices the algorithm runs in time O(n 2 ω), i.e., almost linear in the size of the matrix, where w = w(n) is any function satisfying ω(n) → ∞ as n → ∞. This improves the previous bound of O(n 3 ω) for such matrices. The estimator can also be used to estimate the size of a backtrack tree. 
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