There has been fantastic work done on the Permanent going on for the last two decades.I have been wondering for a while about the possibility of a Smooth P algorithm for the Permanent of Nonnegative Matrices. There is of course the famous JSV algorithm but this is a fpras. Thinking about other work within Smoothed Complexity, a strong hint of being in Smoothed P was the existence of a fpras / Psuedopolynomial algorithm.
Are there any obstructions to the Nonnegative Permanent being in Smoothed P?
Thanks in advance