# A fast algorithm for the gas station problem

## TL;DR

This paper introduces a faster algorithm for the gas station problem, optimizing the pathfinding process with fuel constraints and limited stops, significantly improving computational efficiency over previous methods.

## Contribution

The paper presents an improved algorithm with a complexity of O(Δ n^2 + n^2 log n), enhancing prior solutions for the gas station problem.

## Key findings

- Algorithm runs in O(Δ n^2 + n^2 log n) steps
- Significant speedup over previous algorithms
- Effective handling of fuel and stop constraints

## Abstract

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 $\Delta$ stops for refuelling. In this short paper we provide an algorithm solving the problem in $O(\Delta n^2 + n^2\log{n})$ steps improving an earlier result by Khuller, Malekian and Mestre.