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.