Upgrading FPAUS to perfect sampling under stronger efficiency requirements

Establish whether every fully polynomial almost uniform sampler (FPAUS) can be transformed into a perfect sampling algorithm that satisfies the stronger efficiency notion for perfect sampling advocated in earlier literature (as opposed to the more common notion based only on polynomial expected running time).

Background

The paper adopts the now-standard definition of efficiency for perfect sampling based on expected running time, while noting that earlier works (e.g., Jerrum–Valiant–Vazirani) considered stronger efficiency notions. The authors provide reductions that achieve perfect sampling with polynomial expected time (and high probability), but leave open whether an FPAUS can always be converted to a perfect sampler meeting the stronger requirement.

For self-reducible problems, they discuss how expected-time perfect sampling implies approximate sampling with suitable parameters, yet the general conversion to satisfy stronger efficiency remains unresolved.