NP-Hardness of Rotation Type Cell-Mazes (Special Section of Selected Papers from the 12th Workshop on Circuit and Systems in Karuizawa)

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In this paper, a puzzle called Cell-Maze is analyzed. In this puzzle, cells are arranged in checker board squares. Each cell is rotated when a player arrives at the cell. Cell-Maze asks whether or not a player started from a start cell can reach a goal cell. The reachability problem for ordinary graphs can be easily solved in linear time, however a reachability problem for the network such as Cell-Maze may be extremely difficult. In this paper, NP-hardness of this puzzle is proved. It is proved by reducing Hamiltonian Circuit Problem of directed planar graph G such that each vertex involved in just three arcs. Furthermore, we consider subproblems, which can be solved in polynomial time.
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2000-03-25