Near-linear one-to-all fastest durations with uniform zero delay

Establish whether, for an undirected interval temporal graph with uniform zero delay, an algorithm can compute in $\widetilde{\mathcal O}(M)$ time the durations of fastest temporal paths from a specified source vertex to every target vertex.

Background

The paper presents a $\widetilde{\mathcal O}(M)$ algorithm for computing a fastest temporal path between one specified source-target pair when all delays are zero. The conclusion asks whether a comparable near-linear running time is possible for the one-to-all problem, in which a single source is fixed and fastest-path durations to all target vertices must be computed. The authors note that their profile algorithm cannot directly provide one-to-all profiles in the same time because an individual profile may have size $\Omega(M)$, although it can produce all profiles in $\widetilde{\mathcal O}(nM)$ time.