Polynomial-Time Computability of Poly Density

Ascertain whether the poly density h* of an Optimisation Polyamorous Scheduling instance, defined via the optimal value of the dual linear program in Section 7, can be computed exactly in polynomial time.

Background

The authors define poly density through the dual of a fractional scheduling LP, providing powerful instance-specific lower bounds. While this measure is more informative than classical density for star graphs, its exact computation may be challenging due to the exponential number of matchings.

Determining the complexity of computing h* would clarify whether density-based feasibility checks and lower bounds can be made practical.