Improved approximation or PTAS for the Gasoline problem

Establish whether the Gasoline problem admits an approximation algorithm with ratio strictly better than 2, or whether a polynomial‑time approximation scheme exists.

Background

The Gasoline problem is inspired by Lovász’s puzzle and is NP‑hard. A 2‑approximation algorithm is known, but no stronger guarantees or PTAS are established.

The paper studies heuristics, including an iterative rounding algorithm, and provides counterexamples to a conjectured 2‑approximation for a generalized d‑dimensional version, leaving open whether approximation ratios below 2 or a PTAS are attainable.