BusOut is NP-complete

TL;DR

This paper proves that the decision problem underlying the smartphone game Bus Out is NP-complete, indicating its computational difficulty and intractability for optimal solutions in general.

Contribution

It establishes the NP-completeness of the Bus Out problem and demonstrates the difficulty of approximating the minimum number of parking spots required.

Findings

Bus Out problem is NP-complete.

Hard to approximate the minimum parking spots.

NP-completeness holds even for restricted instances.

Abstract

This study examines the computational complexity of the decision problem modeled on the smartphone game Bus Out. The objective of the game is to load all the passengers in a queue onto appropriate buses using a limited number of bus parking spots by selecting and dispatching the buses on a map. We show that the problem is NP-complete, even for highly restricted instances. We also show that it is hard to approximate the minimum number of parking spots needed to solve a given instance.