• Corpus ID: 11770837

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

  title={The Hardness of the Lemmings Game, or "Oh no, more NP-Completeness Proofs"},
  author={Graham Cormode},
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… 

Figures from this paper

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

Lemmings is PSPACE-complete

Hardness of Modern Games

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.

Classic Nintendo Games are (NP-)Hard

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.

Simplified Harvest Moon is NP-Complete

  • S. Braeger
  • Computer Science
    Tiny Trans. Comput. Sci.
  • 2012
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).

The Computational Complexity of Angry Birds and Similar Physics-Simulation Games

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 origi- nal version of Angry Birds is within NP and therefore also NP-complete.

Lumines is NP-complete : Or at least if your gamepad is broken

Lumines is a popular puzzle game where the player organizes dichromatic 2 × 2 blocks on a rectangular grid by rotating and moving them around the gameboard. A line eventually sweeps the gameboard and

On the complexity of Katamari Damacy

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.

The Computational Complexity of Angry Birds

Classic Nintendo games are (computationally) hard



Tetris is hard, even to approximate

It is proved that in the offline version of Tetris, it is -complete to maximize the number of cleared rows, maximize theNumber of tetrises (quadruples of rows simultaneously filled and cleared), minimize the maximum height of an occupied square, or maximize thenumber of pieces placed before the game ends.

Partial Formalizations And The Lemmings Game

The features of the Lemmings world that make it a challenge to both experimental and theoretical AI and some steps toward formalizing the game using situation calculus are discussed.

Playing Games with Algorithms: Algorithmic Combinatorial Game Theory

Background in combinatorial game theory is reviewed, which analyzes ideal play in perfect-information games and results about the complexity of determining ideal play are surveyed, in terms of both polynomial-time algorithms and computational intractability results.

Sokoban is PSPACE-complete

It is shown that the popular puzzle Sokoban can be used to emulate a linear bounded automata and shows that the puzzles are PSPACE-complete, solving the open problem stated in 1.

On the Complexity of the “ Reflections ” game David Kempe January 2 , 2003

The game “Reflections” is a puzzle game that has been around and entertaining users in various versions for many years. A single player tries to hit a given set of light bulbs with a laser beam, by

The Computational Complexity of Motion Planning

In this paper we show that a generalization of a popular motion planning puzzle called Lunar Lockout is computationally intractable. In particular, we show that the problem is PSPACE-complete. We

Minesweeper is NP-complete

NP-completeness Many programming p rob lems require the design of an algori thm which has a "yes" or "no" ou tput for each input, and there are two classes of p rob l ems that are of grea tes t in teres t for complexi tytheoris ts.

Pushing blocks is np-complete for noncrossing solution paths