Upgrade FPAUS to perfect sampling under stronger efficiency requirements

Determine whether a fully polynomial almost uniform sampler (FPAUS) for a distribution can always be transformed into a perfect sampling algorithm that satisfies the stronger efficiency notion considered in earlier work (such as Jerrum–Valiant–Vazirani), achieving polynomial-time guarantees under that stronger running time requirement rather than only polynomial expected running time.

Background

The paper’s reductions yield perfect sampling algorithms with polynomial expected running time, aligning with much of the modern literature. Earlier work (e.g., Jerrum–Valiant–Vazirani) considered stronger efficiency notions for perfect sampling than expected-time guarantees.

Bridging this gap would establish whether having an FPAUS suffices not only for expected-time perfect sampling but also for meeting the stronger, earlier efficiency requirements, potentially implying more robust worst-case running time guarantees.