Abstract
Lemmings is a computer puzzle game developed by DMA Design and published by Psygnosis in 1991, in which the player has to guide a tribe of lemming creatures to safety through a hazardous landscape, by assigning them specific skills that modify their behavior in different ways. In this paper we study the optimization problem of saving the highest number of lemmings in a given landscape with a given number of available skills.
We prove that the game is PSPACE-complete, even if there is only one lemming to save. We thereby settle an open problem posed by Cormode in 2004, and again by Forišek in 2010. However, if we restrict to levels in which the available Builders, Bashers, and Miners are polynomially many, then the game is solvable in NP.
Furthermore, we show that saving the maximum number of lemmings is APX-hard, even when only Climbers are available. This contrasts with the membership in P of the decision problem restricted to levels with no “deadly areas” (such as water or traps) and only Climbers and Floaters, as previously established by Cormode.
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Viglietta, G. (2014). Lemmings Is PSPACE-Complete. In: Ferro, A., Luccio, F., Widmayer, P. (eds) Fun with Algorithms. FUN 2014. Lecture Notes in Computer Science, vol 8496. Springer, Cham. https://doi.org/10.1007/978-3-319-07890-8_29
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DOI: https://doi.org/10.1007/978-3-319-07890-8_29
Publisher Name: Springer, Cham
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