Recently, due to the widespread diffusion of smart-phones, mobile puzzle games have experienced a huge increase in their popularity. A successful puzzle has to be both captivating and challenging, and it has been suggested that these features are somehow related to their computational complexity [6]. Indeed, many puzzle games – such as Mah-Jongg, Sokoban, Candy Crush, and 2048, to name a few – are known to be NP-hard [3,4,8,12]. In this paper we consider Trainyard: a popular mobile puzzle game whose goal is to get colored trains from their initial stations to suitable destination stations. We prove that the problem of determining whether there exists a solution to a given Trainyard level is NP-hard. We also provide an implementation of our hardness reduction.

Trainyard is NP-Hard / Almanza, Matteo; Leucci, S.; Panconesi, A.. - In: THEORETICAL COMPUTER SCIENCE. - ISSN 0304-3975. - 748:(2018), pp. 66-76. [10.1016/j.tcs.2017.09.039]

Trainyard is NP-Hard

ALMANZA, Matteo;Leucci S.;Panconesi A.
2018

Abstract

Recently, due to the widespread diffusion of smart-phones, mobile puzzle games have experienced a huge increase in their popularity. A successful puzzle has to be both captivating and challenging, and it has been suggested that these features are somehow related to their computational complexity [6]. Indeed, many puzzle games – such as Mah-Jongg, Sokoban, Candy Crush, and 2048, to name a few – are known to be NP-hard [3,4,8,12]. In this paper we consider Trainyard: a popular mobile puzzle game whose goal is to get colored trains from their initial stations to suitable destination stations. We prove that the problem of determining whether there exists a solution to a given Trainyard level is NP-hard. We also provide an implementation of our hardness reduction.
2018
Computational complexity; Puzzle games; Solitaire games; Trainyard
01 Pubblicazione su rivista::01a Articolo in rivista
Trainyard is NP-Hard / Almanza, Matteo; Leucci, S.; Panconesi, A.. - In: THEORETICAL COMPUTER SCIENCE. - ISSN 0304-3975. - 748:(2018), pp. 66-76. [10.1016/j.tcs.2017.09.039]
File allegati a questo prodotto
File Dimensione Formato  
Almanza_Trainyard_2018.pdf

accesso aperto

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 2.45 MB
Formato Adobe PDF
2.45 MB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1291937
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 2
social impact