Efficient pigeonhole conjecture for lattice path matroids

Let $\mathcal{M}$ be the class of lattice path matroids. The class is efficiently pigeonhole when the relevant pigeonhole bounds can be obtained efficiently. Efficient pigeonhole conjecture. The class of lattice path matroids is efficiently pigeonhole. The paper has proved that lattice path matroids are pigeonhole, but states that the stronger property of being strongly pigeonhole has not yet been proved; this conjecture is presented as open.