Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices

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

Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices

I will present a deterministic polynomial time c^n approximation algorithm for the permanent of positive semidefinite matrices where c ~ 4.84. This is through a natural convex programming relaxation and proving a PSD variation of the Van der Waerden's theorem. Joint work with Nima Anari, Shayan Oveis Gharan, and Leonid Gurvitz.Non UBCUnreviewedAuthor affiliation: Stanford UniversityFacult