Abstract
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 polynomial-time algorithm for the approximate (up to subexponential errors) evaluation of the number of perfect matchings.
| Original language | English |
|---|---|
| Pages (from-to) | 2858-2888 |
| Number of pages | 31 |
| Journal | Annals of Probability |
| Volume | 44 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2016 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© Institute of Mathematical Statistics, 2016.
Funding
| Funders | Funder number |
|---|---|
| National Science Foundation | |
| Directorate for Mathematical and Physical Sciences | 1161372 |
Keywords
- Hafnian
- Perfect matching
- Random Gaussian matrices