Corpus ID: 11770837

The Hardness of the Lemmings Game, or "Oh no, more NP-Completeness Proofs"

@inproceedings{Cormode2004TheHO,
  title={The Hardness of the Lemmings Game, or "Oh no, more NP-Completeness Proofs"},
  author={Graham Cormode},
  year={2004}
}
In the computer game ‘Lemmings’, the player must guide a tribe of green-haired lemming creatures to safety, and save them from an untimely demise. We formulate the decision problem which is, given a level of the game, to decide whether it is possible to complete the level (and hence to find a solution to that level). Under certain limitations, this can be decided in polynomial time, but in general the problem is shown to be NP-Hard. This can hold even if there is only a single lemming to save… Expand
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26 Citations
Highly Influential Citations
4
Background Citations
12
Methods Citations
2

26 Citations

Citation Type

Citation Type

Lemmings is PSPACE-complete
  • G. Viglietta
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 2015
TLDR
It is proved that the game is PSPACE-complete, even if there is only one lemming to save, and only Builder and Basher skills are available, and it is shown that saving the maximum number of lemmings is APX-hard, even when only one type of skill is available, whatever this skill is. Expand
Computational Complexity of Two-Dimensional Platform Games
We analyze the computational complexity of various two-dimensional platform games. We state and prove several meta-theorems that identify a class of these games for which the set of solvable levels… Expand
Lemmings Is PSPACE-Complete
TLDR
The optimization problem of saving the highest number of lemmings in a given landscape with a given number of available skills is studied. Expand
Hardness of Modern Games
TLDR
This work considers the complexity properties of modern puzzle games, Hexiom, Cut the Rope and Back to Bed, and gives further insight into the structure of these games and the resulting constructions may be useful in further complexity studies. Expand
Classic Nintendo Games are (NP-)Hard
TLDR
This work proves NP-hardness results for five of Nintendo’s largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pokémon, and observes that several games in the Zelda series are PSPACE-complete. Expand
The Computational Complexity of Angry Birds and Similar Physics-Simulation Games
TLDR
By using a combination of different gadgets within this game’s environment, it is demonstrated that the problem of solving Angry Birds levels is NP-hard, and the original version of Angry Birds is within NP and therefore also NP-complete. Expand
Classic Nintendo Games Are (Computationally) Hard
TLDR
These results apply to generalized versions of Super Mario Bros. 1, 3, Lost Levels, and Super Mario World; Donkey Kong Country 1–3; all Legend of Zelda games; all Metroid games; and all Pokemon role-playing games. Expand
Simplified Harvest Moon is NP-Complete
  • S. Braeger
  • Computer Science, Mathematics
  • Tiny Trans. Comput. Sci.
  • 2012
TLDR
A proof that SHM is NP-complete is presented using the Bounded Knapsack Problem (BKP) and it is shown that there exists a trivial bijection from all instances of BKP to all instance of Simplified Harvest Moon (SHM). Expand
On the complexity of Katamari Damacy
TLDR
The complexity of algorithm-based games has been of interest to computer scientists for a long time and the types of games that typically receive attention are single player puzzle games, two player board games, and mathematical games. Expand
The Computational Complexity of Angry Birds
TLDR
This paper is the first time that a single-player game has been proven EXPTIME-complete, and uses stochastic game engine dynamics to effectively model the real world, or in this case the physics simulator, as the opponent against which the authors are playing. Expand
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