PTAS for Bamboo Garden Trimming or Windows Scheduling

Develop a polynomial-time approximation scheme (PTAS) for the Bamboo Garden Trimming problem or for the Windows Scheduling problem, or establish that no PTAS exists under standard complexity assumptions.

Background

The paper reviews related periodic scheduling problems, noting that both Bamboo Garden Trimming and Windows Scheduling have efficient constant-factor approximations but lack PTAS results.

Establishing PTASs (or proving their impossibility) would significantly advance the state of the art in these foundational periodic scheduling variants and potentially inform algorithms for Polyamorous Scheduling.