Random Gaussian matrices and Hafnian estimators

نویسندگان

  • Mark Rudelson
  • Alex Samorodnitsky
  • Ofer Zeitouni
چکیده

We analyze the behavior of the Barvinok estimator of the hafnian of even dimension, symmetric matrices with nonnegative entries. We introduce a condition under which the Barvinok estimator achieves subexponential errors, and show that this condition is almost optimal. Using that hafnians count the number of perfect matchings in graphs, we conclude that Barvinok’s estimator gives a polynomialtime algorithm for the approximate (up to subexponential errors) evaluation of the number of perfect matchings.

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عنوان ژورنال:
  • CoRR

دوره abs/1409.3905  شماره 

صفحات  -

تاریخ انتشار 2014