Approximating the Permanent

  title={Approximating the Permanent},
  author={Mark Jerrum and Alistair Sinclair},
  journal={SIAM J. Comput.},
A randomised approximation scheme for the permanent of a 0–1s presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the graph. For a wide class of 0–1 matrices the approximation scheme is fully-polynomial, i.e., runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output. This class… 

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