A fast algorithm for the gas station problem

In the gas station problem we want to find the cheapest path between two vertices of an n-vertex graph. Our car has a specific fuel capacity and at each vertex we can fill our car with gas, with the fuel cost depending on the vertex. Furthermore, we are allowed at most ∆ stops for refuelling. In this short paper we provide an algorithm solving the problem in O(∆n2 + n2 logn) steps improving an earlier result by Khuller, Malekian and Mestre.