English

Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices

Combinatorics 2017-04-13 v1 Data Structures and Algorithms Probability Quantum Physics

Abstract

We design a deterministic polynomial time cnc^n approximation algorithm for the permanent of positive semidefinite matrices where c=eγ+14.84c=e^{\gamma+1}\simeq 4.84. We write a natural convex relaxation and show that its optimum solution gives a cnc^n approximation of the permanent. We further show that this factor is asymptotically tight by constructing a family of positive semidefinite matrices.

Keywords

Cite

@article{arxiv.1704.03486,
  title  = {Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices},
  author = {Nima Anari and Leonid Gurvits and Shayan Oveis Gharan and Amin Saberi},
  journal= {arXiv preprint arXiv:1704.03486},
  year   = {2017}
}