Approximation hardness for uniform-delay-one fastest temporal paths

Determine whether the hardness result for computing a fastest temporal path in an undirected interval temporal graph with uniform delay one can be extended to a hardness-of-approximation result.

Background

The paper establishes a conditional fine-grained lower bound for computing an exact fastest temporal path in undirected interval temporal graphs in which every temporal edge has delay one. The reduction distinguishes graphs containing a triangle by whether the optimum duration equals four. The authors then explicitly ask whether this exact-computation hardness can be strengthened to rule out efficient approximation algorithms, leaving the approximation question unresolved.