DIMACS TR: 2004-11

The Hardness of the Lemmings Game

Authors: 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, thus showing that it is hard to approximate the number of saved lemmings to any factor.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2004/2004-11.ps.gz
DIMACS Home Page