Universal Constant-Factor Frequency Scaling for Feasibility

Determine whether there exists a universal constant c ≥ 1 such that for every Decision Polyamorous Scheduling instance (P, R, f), scaling all edge frequencies by c (i.e., replacing each f(e) with c · f(e)) guarantees the existence of a valid periodic schedule.

Background

In Pinwheel Scheduling, increasing each frequency to the next power of two (a constant-factor increase) ensures schedulability with a simple periodic schedule. The paper shows that analogous local strategies fail for general Polyamorous Scheduling and raises the question of whether any universal constant-factor scaling can guarantee feasibility across all instances.

This question addresses a fundamental structural difference between star-graph cases and general graphs, probing whether a global schedule can always be forced by uniform slack.