NP-hardness of rotation type cell-mazes
In paper, a puzzle called Cell-Maze is analyzed. In this puzzle, cells are arranged in checker board squares. Each cell is rotated when a play er 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.
np-hard puzzle maze computational complexity polynomial-time