Reducing the Approximation Gap for OPS

Improve the current bounds for Optimisation Polyamorous Scheduling by reducing the gap between the hardness-of-approximation lower bound (no approximation ratio below 4 unless P = NP) and the O(log n) approximation algorithm, either by designing improved algorithms or by strengthening lower bounds.

Background

The paper establishes the first nontrivial hardness-of-approximation lower bound for a periodic scheduling problem and presents an O(log n) approximation algorithm, but a substantial gap remains between these bounds.

Closing or narrowing this gap would either provide better practical algorithms for OPS or deepen the theoretical understanding of its inapproximability.