1 Introduction
1.1 Related Work
1.2 Our Results
2 Preliminaries
3 Approximating Optimisation Polyamorous Scheduling
3.1 Lower Bounds
3.2 Reduce-Fastest
3.3 Length of schedules
4 Poly Density
4.1 Bounding Poly Density for OPS polycules
4.2 Poly Density of DPS polycules
5 Inapproximability
5.1 Overview of Proof
5.2 Overview of Reduction
5.3 The True Clock & Colour Slots
5.4 Variables
5.5 Flippers
5.6 Duplication of Variables and Constants
5.7 Clauses
5.8 Tension
5.9 Proof of Reduction
6 Conclusion and Open Problems
References