XP approximation for Mim-Width

Determine whether an XP algorithm exists that approximates Mim-Width and its variants within a factor given by some fixed function of the optimum width.

Background

The paper establishes paraNP-completeness for computing Mim-Width, Sim-Width, One-Sided Mim-Width, and their linear counterparts when the optimum is bounded by a constant. This rules out slice-wise polynomial exact computation under the stated hardness framework, but the authors explicitly leave unresolved whether approximation is possible in XP time. The open question concerns the existence of an XP algorithm with approximation factor f(OPT), where f is a fixed function and OPT denotes the optimum width.