NP Membership of Decision Polyamorous Scheduling

Determine whether the Decision Polyamorous Scheduling problem (DPS) belongs to NP by establishing whether every yes-instance admits a polynomial-size certificate verifiable in polynomial time.

Background

While DPS is shown to be NP-hard via multiple reductions, its membership in NP is unclear due to the potential need for exponentially long schedules and the absence of known succinct certificates. The paper situates DPS within PSPACE by constructing a configuration graph and using space-bounded reachability.

This mirrors the situation for Pinwheel Scheduling, for which NP membership is also unknown.