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On the parameterized complexity of a generalized Rush Hour puzzle

By H. Fernau, T. Hagerup, N. Nishimura, P. Ragde and K. Reinhardt


We consider the parameterized complexity of a generalized version of the game Rush Hour, which is a puzzle requiring the player to find a sequence of moves by vehicles to enable a special target vehicle to escape from a grid-shaped game board that may contain obstacles. Although the problem is PSPACE-complete, we demonstrate algorithms that work in polynomial time when either the total number of vehicles or the total number of moves is bounded by a constant. Our contributions are two-fold, entailing the application of ideas of parameterized complexity to games and to motion-planning problems (albeit motion-planning problems of a very constrained nature)

Year: 2003
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