Existence of Constant-Factor Approximation for OPS

Determine whether Optimisation Polyamorous Scheduling admits a polynomial-time constant-factor approximation algorithm that achieves a fixed approximation ratio independent of the instance size and maximum degree.

Background

For Bamboo Garden Trimming (the star-graph special case), increasingly better constant-factor approximation algorithms are known. However, Polyamorous Scheduling on general graphs cannot simply combine local schedules, complicating the design of global approximations.

The authors raise the possibility that efficient constant-factor approximations may not exist for OPS and highlight the lack of current evidence either way, beyond their O(log n) algorithm.

References

Although BGT can be approximated well, since it is in general not possible to combine local schedules into a global schedule for a polycule (as noted above), it is not clear whether Poly Scheduling allows an efficient constant-factor approximation.

— Polyamorous Scheduling (2403.00465 - Gąsieniec et al., 1 Mar 2024) in Section 1.2 (Related Work)