Close the fastest-temporal-path complexity gap

Close the gap between the \Omega(nM) conditional lower bound and the \widetilde{\mathcal O}(mM) best-known upper bound for computing a fastest temporal path in an interval temporal graph.

Background

The paper gives a conditional lower bound of essentially \Omega(nM) for fastest temporal path computation in interval temporal graphs, while the best-known algorithm requires \widetilde{\mathcal O}(mM), where m is the number of underlying edges and M is the number of temporal edge appearances. Since m can be as large as n^2, these bounds leave a substantial complexity gap. The conclusion explicitly asks whether the gap can be closed.